Answer:
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)
