Question

Find the equation of the parabola with vertex at the origin, symmetric with respect to $y-$axis and passing through $(3,-5)$.

Answer 1

The vertex of the parabola is at origin and it is symmetric with respect to $y-$axis

Also, it passes through $(3,-5)$ , a point in the fourth quadrant.

Let its equation be $x^2=-4ay$ ........$\left(1\right)$

As it passes through $(3,-5)$, we get

$3^2=-4a\times -5\Rightarrow a=\frac{9}{20}$

Substituting this value of $a$ in $\left(1\right)$, the equation of the parabola is

$x^2=-4\times \frac{9}{20}y$

or $5x^2=-9y$