Conic Sections Parabola

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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.




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