Answer
(a)
Vertex: $V(-2,2)$
Focus: $F(-1,2)$
Directrix: $x=-3$
(b)
Work Step by Step
Equation of a parabola with horizontal axis and vertex at $(h,k)$:
$(y-k)^2=4p(x-h)$
$(y-2)^2=4(x+2)$
$(y-2)^2=4[x-(-2)]$
$h=-2$
$k=2$
Vertex: $V(h,k)=V(-2,2)$
$4p=4$
$p=1$
The given equation can be obtained by shifting
$y^2=4x$
left 2 units and upward 2 units. In this equation:
Focus: $F(p,0)=F(1,0)$
Directrix: $y=-p=-1$
Now, shift the focus and the directrix 2 units to the left and 2 units upward:
Focus: $F(-1,2)$
Directrix: $x=-3$
