Answer:
The required equation is
.
Step-by-step explanation:
The standard form of the equation of the parabola is
.... (1)
where, (h, k) is vertex and y = k - p is directrix.
It is given that vertex of parabola is (–4, –6) and the directrix is y = 3.
![(-4,-6)=(h,k)](https://tex.z-dn.net/?f=%28-4%2C-6%29%3D%28h%2Ck%29)
On comparing both the sides, we get
![h=-4,k=-6](https://tex.z-dn.net/?f=h%3D-4%2Ck%3D-6)
Directrix of the parabola is
![y=k-p](https://tex.z-dn.net/?f=y%3Dk-p)
Put y=3 and k=-6 in the above equation.
![3=-6-p](https://tex.z-dn.net/?f=3%3D-6-p)
![3+6=-p](https://tex.z-dn.net/?f=3%2B6%3D-p)
![9=-p](https://tex.z-dn.net/?f=9%3D-p)
![-9=p](https://tex.z-dn.net/?f=-9%3Dp)
Substitute h=-4,p=-9 and k=-6 in equation (1).
![(x-(-4))^2=4(-9)(y-(-6))](https://tex.z-dn.net/?f=%28x-%28-4%29%29%5E2%3D4%28-9%29%28y-%28-6%29%29)
![(x+4)^2=-36(y+6)](https://tex.z-dn.net/?f=%28x%2B4%29%5E2%3D-36%28y%2B6%29)
Therefore the required equation is
.