Conic Sections Parabola

Conic Sections Parabola Conic Section parabola is a part of a cone. It is obtained when a 3 dimensional cone is cut. The intersection may be a circle, ellipse, parabola, hyperbola or even a line, point, or line. An parabola is obtained from conic section when the answer to this formula B^2 4 A C is zero and eccentricity is 1. The equation for the conic section parabola is: Y^2 = 4 a x and x^2 = 4ay Eccentricity is always 1 and parametric equation is (a t^2, 2 a t) Example 1: A conic section parabola has a = 2, t = 4. Find the parametric equation coordinates. Solution: In the given problem Parametric equation = (a t^2, 2 a t) Plugging in the values of t and a we get, Parametric = (2) (4)^2, 2 (2) (4) (2) (16), (4) (4) 32, 16 The parametric equation coordinates = (32, 16) Example 2: For a given conic section parabola a = 16 and x = 9. Find the y from the parabolic equation. Solution: For the given problem The parabolic equation is y^2 = 4ax Plugging in the values of a and x we get, y^2 = 4 (16) ( 9 ) y = 2 (4) (3) = 24 The y will be 24 for the given conic section parabola.