Let P(x,y) be a point on the parabola. The definition of a parabola is the squared distance from P to focus F(2,2) equals the squared distance to the directrix x=8.
squared distance from P(x,y) to focus F(2,2)
(x - 2)² + (y - 2)²
squared distance from P(x,y) to the directrix x=8.
(x-8)²
Those are equal in a parabola,
(x - 2)² + (y - 2)² = (x-8)²
x² - 4x + 4 + y² - 4y + 4 = x² - 16x + 64
y² - 4y - 46 = -12x
That's a sideways parabola,
x = -(y² - 4y - 46)/12
