Question

Find the equation of the parabola that satisfies the given conditons:
Focus
Vertex (0,0) passing trhough (5,2) and symmetric with respect to y - axis.

Answer 1

The vertex of the parabola is at (0,0) and it is symmetrical about the y - axis.
$\therefore$ axis of parabola is y - axis.
So the parabola is of the form $x^2=4ay.$
Since the parabola passes through point (5,2)
$\therefore (5{)}^2=4a\times 2\Rightarrow 25=8a\Rightarrow a=\frac{25}{8}$
$x^2\frac{4\times 25}{8}y\Rightarrow x^2=\frac{25}{2}y\Rightarrow 2x^2=25y$