What is the equation of the parabola with focus (-1/4,-2/3) and directrix y=3/4? A. y = -x^2 +8x -7
B. y = -1/2x^2 +14/5x +17/53
C. y = -6/17x^2 - 3/17x +1/51
D. y = -1/6x^2

Given:

Focus of the parabola =

Directrix of the parabola is .

To find:

The equation of the parabola.

Solution:

The equation of the parabola is:

            ...(i)

Where, (h,k) is vertex, (h,k+p) is focus and is the directrix.

It is given that the focus of the parabola is at .

On comparing both sides, we get

           ...(ii)

Directrix of the parabola is . So,

            ...(iii)

Adding (ii) and (iii), we get

Putting in (ii), we get

Putting in (i), we get

On further simplification, we get

Therefore, the equation of the parabola is . Hence, the correct option is C.