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Page 1 Solved Examples on Parabola Q1: The equation of parabola whose focus is (?? , ?? ) and directrix is ?? ?? - ?? ?? + ?? = ?? , is (a) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (b) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (c) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (d) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? Ans: (a) Sol: ?? ?? 2 = ?? ?? 2 ? (?? - 5) 2 + (?? - 3) 2 = ( 3?? - 4?? + 1 v9 + 16 ) 2 ? 25(?? 2 + 25 - 10?? + ?? 2 + 9 - 6?? ) = 9?? 2 + 16?? 2 + 1 - 12???? + 6?? - 8?? - 12???? ? 16?? 2 + 9?? 2 - 256?? - 142 ?? + 24???? + 849 = 0 ? (4?? + 3?? ) 2 - 256?? - 142 ?? + 849 = 0 Q2: The point on the parabola ?? ?? = ?? ?? . Whose distance from the focus is 8 , has ?? -coordinate as (a) 0 (b) 2 (c) 4 (d) 6 Ans: (d) Sol: If ?? (?? 1 , ?? 1 ) is a point on the parabola ?? 2 = 4???? and S is its focus, then ???? = Page 2 Solved Examples on Parabola Q1: The equation of parabola whose focus is (?? , ?? ) and directrix is ?? ?? - ?? ?? + ?? = ?? , is (a) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (b) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (c) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (d) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? Ans: (a) Sol: ?? ?? 2 = ?? ?? 2 ? (?? - 5) 2 + (?? - 3) 2 = ( 3?? - 4?? + 1 v9 + 16 ) 2 ? 25(?? 2 + 25 - 10?? + ?? 2 + 9 - 6?? ) = 9?? 2 + 16?? 2 + 1 - 12???? + 6?? - 8?? - 12???? ? 16?? 2 + 9?? 2 - 256?? - 142 ?? + 24???? + 849 = 0 ? (4?? + 3?? ) 2 - 256?? - 142 ?? + 849 = 0 Q2: The point on the parabola ?? ?? = ?? ?? . Whose distance from the focus is 8 , has ?? -coordinate as (a) 0 (b) 2 (c) 4 (d) 6 Ans: (d) Sol: If ?? (?? 1 , ?? 1 ) is a point on the parabola ?? 2 = 4???? and S is its focus, then ???? = ?? 1 + ?? Here 4?? = 8 ? ?? = 2; ???? = 8 ? 8 = ?? 1 + 2 ? ?? 1 = 6 Q3: If the parabola ?? ?? = ?? ax passes through (-?? , ?? ), then length of its latus rectum is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) 4 Ans: (c) Sol: The point (-3,2) will satisfy the equation ?? 2 = 4???? ? 4 = -12?? ? Latus rectum = 4|?? | = 4 × |- 1 3 | = 4 3 Q4: The equation of the parabola with its vertex at the origin, axis on the ?? - axis and passing through the point (?? , -?? ) is (a) ?? ?? = ???? ?? + ?? (b) ?? ?? = ???? ?? (c) ?? ?? = -???? ?? (d) ?? ?? = -???? ?? + ?? Ans: (c) Sol: Since the axis of parabola is ?? -axis with its vertex at origin. ? Equation of parabola ?? 2 = 4???? . Since it passes through (6, -3) ; ? 36 = -12?? ? ?? = -3 ? Equation of parabola is ?? 2 = -12?? . Q5: The line ?? - ?? = ?? is the directrix of the parabola ?? ?? - ???? + ?? = ?? . Then one of the values of ?? is (a) ?? ?? (b) 8 (c) 4 Page 3 Solved Examples on Parabola Q1: The equation of parabola whose focus is (?? , ?? ) and directrix is ?? ?? - ?? ?? + ?? = ?? , is (a) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (b) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (c) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (d) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? Ans: (a) Sol: ?? ?? 2 = ?? ?? 2 ? (?? - 5) 2 + (?? - 3) 2 = ( 3?? - 4?? + 1 v9 + 16 ) 2 ? 25(?? 2 + 25 - 10?? + ?? 2 + 9 - 6?? ) = 9?? 2 + 16?? 2 + 1 - 12???? + 6?? - 8?? - 12???? ? 16?? 2 + 9?? 2 - 256?? - 142 ?? + 24???? + 849 = 0 ? (4?? + 3?? ) 2 - 256?? - 142 ?? + 849 = 0 Q2: The point on the parabola ?? ?? = ?? ?? . Whose distance from the focus is 8 , has ?? -coordinate as (a) 0 (b) 2 (c) 4 (d) 6 Ans: (d) Sol: If ?? (?? 1 , ?? 1 ) is a point on the parabola ?? 2 = 4???? and S is its focus, then ???? = ?? 1 + ?? Here 4?? = 8 ? ?? = 2; ???? = 8 ? 8 = ?? 1 + 2 ? ?? 1 = 6 Q3: If the parabola ?? ?? = ?? ax passes through (-?? , ?? ), then length of its latus rectum is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) 4 Ans: (c) Sol: The point (-3,2) will satisfy the equation ?? 2 = 4???? ? 4 = -12?? ? Latus rectum = 4|?? | = 4 × |- 1 3 | = 4 3 Q4: The equation of the parabola with its vertex at the origin, axis on the ?? - axis and passing through the point (?? , -?? ) is (a) ?? ?? = ???? ?? + ?? (b) ?? ?? = ???? ?? (c) ?? ?? = -???? ?? (d) ?? ?? = -???? ?? + ?? Ans: (c) Sol: Since the axis of parabola is ?? -axis with its vertex at origin. ? Equation of parabola ?? 2 = 4???? . Since it passes through (6, -3) ; ? 36 = -12?? ? ?? = -3 ? Equation of parabola is ?? 2 = -12?? . Q5: The line ?? - ?? = ?? is the directrix of the parabola ?? ?? - ???? + ?? = ?? . Then one of the values of ?? is (a) ?? ?? (b) 8 (c) 4 (d) ?? ?? Ans: (c) Sol: The parabola is ?? 2 = 4 ?? 4 (?? - 8 ?? ). Putting ?? = ?? , ?? - 8 ?? = ?? . The equation is ?? 2 = 4 · ?? 4 · ?? ? The directrix is ?? + ?? 4 = 0 i.e., ?? - 8 ?? + ?? 4 = 0. But ?? - 1 = 0 is the directrix. So 8 ?? - ?? 4 = 1 ? ?? = -8,4 Q6: The ends of a line segment are ?? (?? , ?? ) and ?? (?? , ?? ). ?? is a point on the line segment ???? such that ???? : ???? = ?? : ?? . If ?? is an interior point of the parabola ?? ?? = ?? ?? , then (a) ?? ? (?? , ?? ) (b) ?? ? (- ?? ?? , ?? ) (c) ?? ? ( ?? ?? , ?? ?? ) (d) None of these Ans: (a) Sol: ?? = (1, 1+3?? 1+?? ) It is an interior point of ?? 2 - 4?? = 0 iff ( 1+3?? 1+?? ) 2 - 4 < 0 ? ( 1 + 3?? 1 + ?? - 2) ( 1 + 3?? 1 + ?? + 2) < 0 ? ( ?? - 1 1 + ?? ) ( 5?? + 3 1 + ?? ) < 0 ? (?? - 1)(?? + 3 5 ) < 0 Therefore, - 3 5 < ?? < 1. But ?? > 0 ? 0 < ?? < 1 ? ?? ? (0,1). Q7: The equation of the tangent to the parabola ?? ?? = ???? ?? , which is perpendicular to the line ?? = ?? ?? + ?? is (a) ?? - ?? ?? + ?? = ?? (b) ?? ?? - ?? + ???? = ?? (c) ?? ?? + ?? - ???? = ?? (d) ?? ?? + ?? + ???? = ?? Ans: (a) Page 4 Solved Examples on Parabola Q1: The equation of parabola whose focus is (?? , ?? ) and directrix is ?? ?? - ?? ?? + ?? = ?? , is (a) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (b) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (c) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (d) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? Ans: (a) Sol: ?? ?? 2 = ?? ?? 2 ? (?? - 5) 2 + (?? - 3) 2 = ( 3?? - 4?? + 1 v9 + 16 ) 2 ? 25(?? 2 + 25 - 10?? + ?? 2 + 9 - 6?? ) = 9?? 2 + 16?? 2 + 1 - 12???? + 6?? - 8?? - 12???? ? 16?? 2 + 9?? 2 - 256?? - 142 ?? + 24???? + 849 = 0 ? (4?? + 3?? ) 2 - 256?? - 142 ?? + 849 = 0 Q2: The point on the parabola ?? ?? = ?? ?? . Whose distance from the focus is 8 , has ?? -coordinate as (a) 0 (b) 2 (c) 4 (d) 6 Ans: (d) Sol: If ?? (?? 1 , ?? 1 ) is a point on the parabola ?? 2 = 4???? and S is its focus, then ???? = ?? 1 + ?? Here 4?? = 8 ? ?? = 2; ???? = 8 ? 8 = ?? 1 + 2 ? ?? 1 = 6 Q3: If the parabola ?? ?? = ?? ax passes through (-?? , ?? ), then length of its latus rectum is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) 4 Ans: (c) Sol: The point (-3,2) will satisfy the equation ?? 2 = 4???? ? 4 = -12?? ? Latus rectum = 4|?? | = 4 × |- 1 3 | = 4 3 Q4: The equation of the parabola with its vertex at the origin, axis on the ?? - axis and passing through the point (?? , -?? ) is (a) ?? ?? = ???? ?? + ?? (b) ?? ?? = ???? ?? (c) ?? ?? = -???? ?? (d) ?? ?? = -???? ?? + ?? Ans: (c) Sol: Since the axis of parabola is ?? -axis with its vertex at origin. ? Equation of parabola ?? 2 = 4???? . Since it passes through (6, -3) ; ? 36 = -12?? ? ?? = -3 ? Equation of parabola is ?? 2 = -12?? . Q5: The line ?? - ?? = ?? is the directrix of the parabola ?? ?? - ???? + ?? = ?? . Then one of the values of ?? is (a) ?? ?? (b) 8 (c) 4 (d) ?? ?? Ans: (c) Sol: The parabola is ?? 2 = 4 ?? 4 (?? - 8 ?? ). Putting ?? = ?? , ?? - 8 ?? = ?? . The equation is ?? 2 = 4 · ?? 4 · ?? ? The directrix is ?? + ?? 4 = 0 i.e., ?? - 8 ?? + ?? 4 = 0. But ?? - 1 = 0 is the directrix. So 8 ?? - ?? 4 = 1 ? ?? = -8,4 Q6: The ends of a line segment are ?? (?? , ?? ) and ?? (?? , ?? ). ?? is a point on the line segment ???? such that ???? : ???? = ?? : ?? . If ?? is an interior point of the parabola ?? ?? = ?? ?? , then (a) ?? ? (?? , ?? ) (b) ?? ? (- ?? ?? , ?? ) (c) ?? ? ( ?? ?? , ?? ?? ) (d) None of these Ans: (a) Sol: ?? = (1, 1+3?? 1+?? ) It is an interior point of ?? 2 - 4?? = 0 iff ( 1+3?? 1+?? ) 2 - 4 < 0 ? ( 1 + 3?? 1 + ?? - 2) ( 1 + 3?? 1 + ?? + 2) < 0 ? ( ?? - 1 1 + ?? ) ( 5?? + 3 1 + ?? ) < 0 ? (?? - 1)(?? + 3 5 ) < 0 Therefore, - 3 5 < ?? < 1. But ?? > 0 ? 0 < ?? < 1 ? ?? ? (0,1). Q7: The equation of the tangent to the parabola ?? ?? = ???? ?? , which is perpendicular to the line ?? = ?? ?? + ?? is (a) ?? - ?? ?? + ?? = ?? (b) ?? ?? - ?? + ???? = ?? (c) ?? ?? + ?? - ???? = ?? (d) ?? ?? + ?? + ???? = ?? Ans: (a) Sol: A line perpendicular to the given line is 3?? + ?? = ?? ? ?? = - 1 3 ?? + ?? 3 Here ?? = - 1 3 , ?? = ?? 3 . If we compare ?? 2 = 16?? with ?? 2 = 4???? , then ?? = 4 Condition for tangency is ?? = ?? ?? ? ?? 3 = 4 (-1/3) ? ?? = -36 … Required equation is ?? + 3?? + 36 = 0. Q8: Two tangents are drawn from the point (-?? , -?? ) to the parabola ?? ?? = ?? ?? . If ?? is the angle between these tangents, then tan ?? = (a) 3 (b) ?? /?? (c) 2 (d) ½ Ans: (a) Sol: Equation of pair of tangent from (-2, -1) to the parabola is given by SS 1 = ?? 2 i.e. (?? 2 - 4?? )(1 + 8) = [?? (-1) - 2(?? - 2)] 2 ? 9?? 2 - 36?? = [-?? - 2?? + 4] 2 ? 9?? 2 - 36?? = ?? 2 + 4?? 2 + 16 + 4???? - 16?? - 8?? ? 4?? 2 - 8?? 2 + 4???? + 20?? - 8?? + 16 = 0 ? tan ?? = | 2vh 2 - ???? ?? + ?? | = | 2v4 - 4(-8) 4 - 8 | = | 12 -4 | = 3 Q9: If ( ?? ?? ) ?? /?? + ( ?? ?? ) ?? /?? = v?? ?? , then the angle of intersection of the parabola ?? ?? = ?? ???? and ?? ?? = ?? ???? at a point other than the origin is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) None of these Ans: (b) Sol: Given parabolas are ?? 2 = 4???? … ..(i) and ?? 2 = 4???? …… (ii) These meet at the points (0,0), (4?? 1/3 ?? 2/3 , 4?? 2/3 ?? 1/3 ) Tangent to (i) at (4?? 1/3 ?? 2/3 , 4?? 2/3 ?? 1/3 ) is ?? . 4?? 2/3 ?? 1/3 = 2?? (?? + 4?? 2/3 ?? 1/3 ) Page 5 Solved Examples on Parabola Q1: The equation of parabola whose focus is (?? , ?? ) and directrix is ?? ?? - ?? ?? + ?? = ?? , is (a) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (b) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (c) (?? ?? + ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? (d) (?? ?? - ?? ?? ) ?? - ?????? ?? - ?????? ?? + ?????? = ?? Ans: (a) Sol: ?? ?? 2 = ?? ?? 2 ? (?? - 5) 2 + (?? - 3) 2 = ( 3?? - 4?? + 1 v9 + 16 ) 2 ? 25(?? 2 + 25 - 10?? + ?? 2 + 9 - 6?? ) = 9?? 2 + 16?? 2 + 1 - 12???? + 6?? - 8?? - 12???? ? 16?? 2 + 9?? 2 - 256?? - 142 ?? + 24???? + 849 = 0 ? (4?? + 3?? ) 2 - 256?? - 142 ?? + 849 = 0 Q2: The point on the parabola ?? ?? = ?? ?? . Whose distance from the focus is 8 , has ?? -coordinate as (a) 0 (b) 2 (c) 4 (d) 6 Ans: (d) Sol: If ?? (?? 1 , ?? 1 ) is a point on the parabola ?? 2 = 4???? and S is its focus, then ???? = ?? 1 + ?? Here 4?? = 8 ? ?? = 2; ???? = 8 ? 8 = ?? 1 + 2 ? ?? 1 = 6 Q3: If the parabola ?? ?? = ?? ax passes through (-?? , ?? ), then length of its latus rectum is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) 4 Ans: (c) Sol: The point (-3,2) will satisfy the equation ?? 2 = 4???? ? 4 = -12?? ? Latus rectum = 4|?? | = 4 × |- 1 3 | = 4 3 Q4: The equation of the parabola with its vertex at the origin, axis on the ?? - axis and passing through the point (?? , -?? ) is (a) ?? ?? = ???? ?? + ?? (b) ?? ?? = ???? ?? (c) ?? ?? = -???? ?? (d) ?? ?? = -???? ?? + ?? Ans: (c) Sol: Since the axis of parabola is ?? -axis with its vertex at origin. ? Equation of parabola ?? 2 = 4???? . Since it passes through (6, -3) ; ? 36 = -12?? ? ?? = -3 ? Equation of parabola is ?? 2 = -12?? . Q5: The line ?? - ?? = ?? is the directrix of the parabola ?? ?? - ???? + ?? = ?? . Then one of the values of ?? is (a) ?? ?? (b) 8 (c) 4 (d) ?? ?? Ans: (c) Sol: The parabola is ?? 2 = 4 ?? 4 (?? - 8 ?? ). Putting ?? = ?? , ?? - 8 ?? = ?? . The equation is ?? 2 = 4 · ?? 4 · ?? ? The directrix is ?? + ?? 4 = 0 i.e., ?? - 8 ?? + ?? 4 = 0. But ?? - 1 = 0 is the directrix. So 8 ?? - ?? 4 = 1 ? ?? = -8,4 Q6: The ends of a line segment are ?? (?? , ?? ) and ?? (?? , ?? ). ?? is a point on the line segment ???? such that ???? : ???? = ?? : ?? . If ?? is an interior point of the parabola ?? ?? = ?? ?? , then (a) ?? ? (?? , ?? ) (b) ?? ? (- ?? ?? , ?? ) (c) ?? ? ( ?? ?? , ?? ?? ) (d) None of these Ans: (a) Sol: ?? = (1, 1+3?? 1+?? ) It is an interior point of ?? 2 - 4?? = 0 iff ( 1+3?? 1+?? ) 2 - 4 < 0 ? ( 1 + 3?? 1 + ?? - 2) ( 1 + 3?? 1 + ?? + 2) < 0 ? ( ?? - 1 1 + ?? ) ( 5?? + 3 1 + ?? ) < 0 ? (?? - 1)(?? + 3 5 ) < 0 Therefore, - 3 5 < ?? < 1. But ?? > 0 ? 0 < ?? < 1 ? ?? ? (0,1). Q7: The equation of the tangent to the parabola ?? ?? = ???? ?? , which is perpendicular to the line ?? = ?? ?? + ?? is (a) ?? - ?? ?? + ?? = ?? (b) ?? ?? - ?? + ???? = ?? (c) ?? ?? + ?? - ???? = ?? (d) ?? ?? + ?? + ???? = ?? Ans: (a) Sol: A line perpendicular to the given line is 3?? + ?? = ?? ? ?? = - 1 3 ?? + ?? 3 Here ?? = - 1 3 , ?? = ?? 3 . If we compare ?? 2 = 16?? with ?? 2 = 4???? , then ?? = 4 Condition for tangency is ?? = ?? ?? ? ?? 3 = 4 (-1/3) ? ?? = -36 … Required equation is ?? + 3?? + 36 = 0. Q8: Two tangents are drawn from the point (-?? , -?? ) to the parabola ?? ?? = ?? ?? . If ?? is the angle between these tangents, then tan ?? = (a) 3 (b) ?? /?? (c) 2 (d) ½ Ans: (a) Sol: Equation of pair of tangent from (-2, -1) to the parabola is given by SS 1 = ?? 2 i.e. (?? 2 - 4?? )(1 + 8) = [?? (-1) - 2(?? - 2)] 2 ? 9?? 2 - 36?? = [-?? - 2?? + 4] 2 ? 9?? 2 - 36?? = ?? 2 + 4?? 2 + 16 + 4???? - 16?? - 8?? ? 4?? 2 - 8?? 2 + 4???? + 20?? - 8?? + 16 = 0 ? tan ?? = | 2vh 2 - ???? ?? + ?? | = | 2v4 - 4(-8) 4 - 8 | = | 12 -4 | = 3 Q9: If ( ?? ?? ) ?? /?? + ( ?? ?? ) ?? /?? = v?? ?? , then the angle of intersection of the parabola ?? ?? = ?? ???? and ?? ?? = ?? ???? at a point other than the origin is (a) ?? /?? (b) ?? /?? (c) ?? /?? (d) None of these Ans: (b) Sol: Given parabolas are ?? 2 = 4???? … ..(i) and ?? 2 = 4???? …… (ii) These meet at the points (0,0), (4?? 1/3 ?? 2/3 , 4?? 2/3 ?? 1/3 ) Tangent to (i) at (4?? 1/3 ?? 2/3 , 4?? 2/3 ?? 1/3 ) is ?? . 4?? 2/3 ?? 1/3 = 2?? (?? + 4?? 2/3 ?? 1/3 ) Slope of the tangent (?? 1 ) = 2?? 4?? 2/3 ?? 1/3 = ?? 1/3 2?? 1/3 Tangent to (ii) at (4?? 1/3 ?? 2/3 , 4?? 2/3 ?? 1/3 ) is ?? · 4?? 1/3 ?? 2/3 = 2?? (?? + 4?? 2/3 ?? 1/3 ) Slope of the tangent (?? 2 ) = 2?? 1/3 ?? 1/3 If ?? is the angle between the two tangents, then ? tan ?? = | ?? 1 -?? 2 1+?? 1 ?? 2 | = | ?? 1/3 2?? 1/3 - 2?? 1/3 ?? 1/3 1+ ?? 1/3 2?? 1/3 · 2?? 1/3 ?? 1/3 | = 3 2 · 1 ( ?? ?? ) 1/3 + ( ?? ?? ) 1/3 = 3 2 · 1 v3 2 = v3; ? ?? = 60 ° = ?? 3 Q10: The equation of the common tangent touching the circle (?? - ?? ) ?? + ?? ?? = ?? and the parabola ?? ?? = ?? ?? above the ?? -axis, is (a) v?? ?? = ?? ?? + ?? (b) v?? ?? = -(?? + ?? ) (c) v?? ?? = ?? + ?? (d) v?? ?? = -(?? ?? + ?? ) Ans: (c) Sol: Any tangent to ?? 2 = 4?? is ?? = ???? + 1 ?? . It touches the circle if 3 = | 3?? + 1 ?? v1+?? 2 | or 9(1 + ?? 2 ) = (3?? + 1 ?? ) 2 or 1 ?? 2 = 3, ? ?? = ± 1 v3Read More
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FAQs on Solved Examples: Parabola - Mathematics (Maths) for JEE Main & Advanced
| 1. What is a parabola in mathematics? |  |
Ans. A parabola is a U-shaped curve that can be represented by a quadratic equation of the form y = ax^2 + bx + c. It is a conic section formed by the intersection of a plane parallel to the side of a cone.
| 2. How do you find the vertex of a parabola? | |
Ans. The vertex of a parabola can be found using the formula x = -b/2a, where the x-coordinate of the vertex is -b/2a. To find the y-coordinate, substitute the x-coordinate back into the equation of the parabola.
| 3. What is the focus of a parabola? | |
Ans. The focus of a parabola is a fixed point located on the axis of symmetry of the parabola. It is equidistant from the directrix as it is from any point on the parabola.
| 4. How do you determine if a parabola opens upwards or downwards? | |
Ans. The direction in which a parabola opens is determined by the sign of the coefficient of x^2 in the equation. If the coefficient is positive, the parabola opens upwards; if it is negative, the parabola opens downwards.
| 5. What is the axis of symmetry of a parabola? | |
Ans. The axis of symmetry of a parabola is a vertical line that passes through the vertex of the parabola. It divides the parabola into two symmetrical halves. The equation of the axis of symmetry is x = -b/2a.
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