Answer
(a)
Vertex: $V(h,k)=V(-3,-2)$
Focus: $F(-3,-7)$
Directrix: $y=3$
Work Step by Step
Equation of a parabola with vertical axis and vertex at $(h,k)$:
$(x-h)^2=4p(y-k)$
$(x+3)^2=-20(y+2)$
$[x-(-3)]^2=-20[y-(-2)]$
$h=-3$
$k=-2$
Vertex: $V(h,k)=V(-3,-2)$
$4p=-20$
$p=-5$
The given equation can be obtained by shifting
$x^2=-20y$
legft 3 units and downward 2 units. In this equation:
Focus: $F(0,p)=F(0,-5)$
Directrix: $y=-p=5$
Now, shift the focus and the directrix 3 units to the left and 2 units downward:
Focus: $F(-3,-7)$
Directrix: $y=3$
