Question

The vertex of the parabola (y + a)² = 8a (x − a) is
(a) (−a, −a)
(b) (a, −a)
(c) (−a, a)
(d) none of these

Answer 1

(b) (a, −a)

Given:
The equation of the parabola is (y + a)² = 8a (x − a).

Putting $X=x-a,Y=y+a$:

$Y^2=8aX$

Vertex = $\left(X=0,Y=0\right)=\left(x-a=0,y+a=0\right)=\left(x=a,y=-a\right)$

Hence, the vertex is at (a, −a).