Class 11

Math

3D Geometry

Conic Sections

Find the equation of the parabola that satisfies the following conditions: Vertex $(0,0)$ passing through $(5,2)$ and symmetric with respect to $y$- axis

The parabola passes through point $(5,2)$ which lies in the first quadrant

Therefore, the equation of the parabola is of the form $x_{2}=4ay$

Point $(5,2)$ must satisfy the equation $x_{2}=4ay$

$∴(5)_{2}=4×a×2$

$⇒25=8a$

$⇒a=825 $

Thus, the equation of the parabola is

$x_{2}=4(825 )y$

$2x_{2}=25y$