A parabola can be drawn given a focus of (5, -7) and a directrix of x=1. Write the equation of the parabola in any form.

x = 1/8(y^2 + 14y + 73)

Step-by-step explanation:

Take any point on the curve (x, y). This is a parabola that opens to the right and contains  terms in x and y^2.

The distance of this point from the focus = its distance from the directrix, so:

sqrt [( x - 5)^2 + (y + 7)^2) = (x - 1)

Squaring both sides:

(x - 5)^2 + (y + 7)^2 = (x - 1)^2

x^2 -10x + 25 + y^2 + 14y + 49 = x^2 - 2x + 1

y^2 + 14y + 73 = 8x

x = 1/8(y^2 + 14y + 73)

answer: can and shows the work

step-by-step explanation: