Answer with explanation:
Vertex of the parabola =(0,0)
Parabola is opening Downwards, in negative direction of y axis.
Equation of the parabola can be written as
x²= -4 a y
Where, (0,-a) is the focus of the parabola.
Line, x=0 is line of symmetry of the parabola,which divides the parabola in two equal halves.
Parabola passes through points (-2,-16) and (2, -16).
(-2)²= -4 a *(-16)
![4= 64a\\\\a=\frac{1}{16}](https://tex.z-dn.net/?f=4%3D%2064a%5C%5C%5C%5Ca%3D%5Cfrac%7B1%7D%7B16%7D)
So, focus of the parabola is
.
Required equation of the parabola is
![x^{2} =-4 \times \frac{1}{16}y\\\\4x^{2} =-y](https://tex.z-dn.net/?f=x%5E%7B2%7D%20%3D-4%20%5Ctimes%20%5Cfrac%7B1%7D%7B16%7Dy%5C%5C%5C%5C4x%5E%7B2%7D%20%3D-y)