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A parabola passes through the points (0,4),(1,9) and (−2,6). Also, the axis of this curve is parallel to the ordinate. The equation of the parabola is
- a)
- b)
- c)
- d)
Correct answer is option 'B'. Can you explain this answer?
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A parabola passes through the points (0,4),(1,9) and (−2,6). Als...
Let the vertex of the parabola be the point (h,k) and length of its latus rectum be 4a.
Since its axis is parallel to y - axis, its equation can be written as
(x−h)2 = 4a(y−k) ..... (1)
It passes through the given points (0,4),(1,9) and (−2,6)
∴(0−h)2=4a(4−k)
⇒h2=4a(4−k) ...... (2)
Since its axis is parallel to y - axis, its equation can be written as
(x−h)2 = 4a(y−k) ..... (1)
It passes through the given points (0,4),(1,9) and (−2,6)
∴(0−h)2=4a(4−k)
⇒h2=4a(4−k) ...... (2)
(1−h)2=4a(9−k)
⇒1−2h+h2=4a(9−k) ...... (3)
⇒1−2h+h2=4a(9−k) ...... (3)
(−2−h)2=4a(6−k)
⇒4+4h+h2=4a(6−k) ...... (4)
Subtracting (2),(3) and (3),(4) we have
1−2h=20a ..... (5) and 3+6h=−12a i.e. 1+2h=−4a ..... (6)
Then solving (5) and (6), we get
a= 1/8, and h=−3/4
Substituting in any of the equations (2),(3) and (4), we get
k= 8/23
Substituting in (1), the equation of parabola is
⇒4+4h+h2=4a(6−k) ...... (4)
Subtracting (2),(3) and (3),(4) we have
1−2h=20a ..... (5) and 3+6h=−12a i.e. 1+2h=−4a ..... (6)
Then solving (5) and (6), we get
a= 1/8, and h=−3/4
Substituting in any of the equations (2),(3) and (4), we get
k= 8/23
Substituting in (1), the equation of parabola is
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A parabola passes through the points (0,4),(1,9) and (−2,6). Also, the axis of this curve is parallel to the ordinate. The equation of the parabola isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?
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A parabola passes through the points (0,4),(1,9) and (−2,6). Also, the axis of this curve is parallel to the ordinate. The equation of the parabola isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? for JEE 2024 is part of JEE preparation. The Question and answers have been prepared according to the JEE exam syllabus. Information about A parabola passes through the points (0,4),(1,9) and (−2,6). Also, the axis of this curve is parallel to the ordinate. The equation of the parabola isa)b)c)d)Correct answer is option 'B'. Can you explain this answer? covers all topics & solutions for JEE 2024 Exam. Find important definitions, questions, meanings, examples, exercises and tests below for A parabola passes through the points (0,4),(1,9) and (−2,6). Also, the axis of this curve is parallel to the ordinate. The equation of the parabola isa)b)c)d)Correct answer is option 'B'. Can you explain this answer?.
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