Question

Find the equation of the parabola with vertex at origin, symmetric with respect to $y-$axis and passing through $(4,-3)$

Answer 1

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

Also, it passes through $(4,-3)$ , a point in the fourth quadrant.

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

As it passes through $(4,-3)$, we get

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

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

$x^2=-4\times \frac{4}{3}y$

or $3x^2=-16y$