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Equation of Parabola - Conic Sections, Math, Class 11 Video Lecture

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FAQs on Equation of Parabola - Conic Sections, Math, Class 11 Video Lecture

1. What is the equation of a parabola?
Ans. The equation of a parabola is given by y = ax^2 + bx + c, where a, b, and c are constants. This equation represents a U-shaped curve in a coordinate plane.
2. How do I determine the direction of a parabola?
Ans. The direction of a parabola can be determined by the coefficient of the x^2 term in its equation. If the coefficient is positive, the parabola opens upwards. If the coefficient is negative, the parabola opens downwards.
3. What are the focus and directrix of a parabola?
Ans. The focus and directrix are two important elements of a parabola. The focus is a fixed point on the axis of symmetry, and the directrix is a straight line perpendicular to the axis of symmetry. The distance from any point on the parabola to the focus is equal to the perpendicular distance to the directrix.
4. How can I find the vertex of a parabola?
Ans. The vertex of a parabola can be found using the formula x = -b/2a, where a and b are the coefficients of the quadratic equation. This x-coordinate of the vertex can then be substituted into the equation to find the y-coordinate.
5. Can a parabola intersect the x-axis at more than two points?
Ans. No, a parabola can intersect the x-axis at most two points. These points are called the x-intercepts or roots of the parabola. If the parabola does not intersect the x-axis, it is called a "degenerate" parabola.
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