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)

y= 2x+7

changed to y= 5x +7

as slope is increased from 2 to 5

therefore it would be less steeper

so, option d) is correct