Write the equation for a parabola with a focus at (6,-4) and a directrix at y= -7

Given:

The focus of the parabola is at (6,-4).

Directrix at y=-7.

To find:

The equation of the parabola.

Solution:

The general equation of a parabola is:

                 ...(i)

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

The focus of the parabola is at (6,-4).

On comparing both sides, we get

                           ...(ii)

Directrix at y=-7. So,

                           ...(iii)

Adding (ii) and (iii), we get

Putting in (ii), we get

Putting in (i), we get

Therefore, the equation of the parabola is .

y = 5x + 17

step-by-step explanation:

a perpendicular line will be the opposite reciprocal slope of the given equation.   the slope given is -1/5 so the opposite reciprocal is 5

find b:

7 = 5 (-2) + b

7 = -10 + b

17 = b

write equation

y = 5x + 17