Question

12. Write the equation of a parabola with vertex at (2, -3) and focus at (2,5),

Answer 1

Step-by-step explanation:

The basic form of equation:

(x-h)²=4a(y-k),

(h,k)=coordinates of vertex

(h, k+a) = coordinate of focus

For given parabola:

axis of symmetry: x=2

(h, k) =(2,-3)

(h, k+a)=(2,5)

k+a=5

-3+a=5

a=8(distance from vertex to focus on the axis of symmetry)

equation: (x-2)²=4×8(y+3)

(x-2)²= 32(y+3)