Question

Find the equation of parabola vertex $(0,0)$, passing through $(5,2)$ and symmetric with respect to $y-axis$.

Answer 1

Axis is along y-axis

$\therefore$ Equation of parabola

$x^2=4ay$ (since $(0,0)$ is vertex)

$\therefore 25=4a\left(2\right)$

$\therefore 4a=\frac{25}{2}$

$\therefore$ Equation of parabola:-

$x^2=\frac{25}{2}y$.