What is the equation of the parabola with focus(1, 1/2)
and directrix y = 3?
A. Y=x^2+17x-1
B. Y=-3/16x^2
C. Y=1/5x^2+2/5x+31/20
D. Y=-3/5x^2-14/31x+71/16

Given:

Focus of a parabola =

Directrix:

To find:

The equation of the parabola.

Solution:

The equation of a vertical parabola is:

           ...(A)

Where, is center, is focus and is the directrix.

On comparing the focus, we get

          ...(i)

On comparing the directrix, we get

             ...(ii)

Adding (i) and (ii), we get

Putting is (i), we get

Putting in (A), we get

On further simplification, we get

Therefore, the equation of the parabola is .

Note: Option C is correct but the leading coefficient should be negative.

unless if u could do my questions, if not i wouldn't want to