12. Write the equation of a parabola with vertex at

(2, - 3) and focus at (2,5),

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)