Find the vertex focus and Ihe directrix of the parabola x22
Find the vertex, focus and Ihe directrix of the parabola (x-2)^2 = -8(y+3). Graph the parabola.
Solution
(x-2)2=-8(y+3)
(-1/8)(x-2)2=y+3
y=(-1/8)(x-2)2 -3
comparing it with equation of parabola which is
y=a(x-h)^2 + k
we get vertex=(2,-3)
1/(4p)=-1/8
4p=-8
p=-2
Focus=(h,k+p)=(2,-3-2)=(2,-5)
directrix,y=k-p
y= -3+2=-1
y=-1
