Answer:
The equation of parabola is \(y^2=-32x\).
Step-by-step explanation:
It is given that the directrix of the parabola is x = 8 and focus is (-8, 0).
Since directrix is x=8, which a vertical line therefore the parabola is algo the x-axis.
The standard for of the parabola is
\((y-k)^2=4p(x-h)\)
Where (h+p,k) is focus and \(x=h-p\) is the directrix.
Since focus of the parabola is (-8,0)
\((h+p,k)=(-8,0)\)
\(k=0\)
\(h+p=-8\) .... (1)
The directrix of the parabola is x= 8
\(h-p=8\) .... (2)
Add equation (1) and (2).
\(2h=0\)
\(h=0\)
Put this value in equation 1.
\(p=-8\)
Therefore h=0, k=0 and p=-8.
\((y-0)^2=4(-8)(x-0)\)
\(y^2=-32x\)
Therefore equation of parabola is \(y^2=-32x\).
