Given, focus is (-6, 6) and vertex is (-2, 2)

Let (a,b) be the intersection of axis and directrix.

vertex is (-2, 2) which is mid point of line joining (a,b) and focus (-6, 6)

Hence by applying mid point formula a = 2, b =10

=> (a, b) = (2, 10)

slope of axis m₁ = 1/2

slope of directrix m₂ = -2        {since it is perpndicular to axis }

Now, equation of directrix

     y - 10 = -2(x - 2)

=> y - 10 = -2x + 4

=> y - 10 - 4 = -2x

=> y - 16 = -2x

=> 2x + y = 16

=> 2x + y - 16 = 0

Let P (x, y) be any point on the required parabola and let PM be the length of the perpendicular from P on the directrix

Then, SP = PM

=> SP² = PM²

=> (x + 6)² + (y - 6) = {(2x + y - 16) /{√(2² + 1² )}²

=> x² + 36 + 12x + y² + 36 - 12y = (4x² + y² + 256 + 4xy - 32y - 64x)/5

=> x² + y² + 12x - 12y + 72 = (4x² + y² + 4xy - 32y - 64x + 256)/5

=> 5(x² + y² + 12x - 12y + 72) = 4x² + y² + 4xy - 32y - 64x + 256

=> 5x² + 5y² + 60x - 60y + 360 = 4x² + y² + 4xy - 32y - 64x + 256

=> 5x² + 5y² + 60x - 60y + 360 - 4x² - y² - 4xy + 32y + 64x - 256 = 0

=> x² + 4y² - 4xy + 124x - 28y + 104 = 0

This is the required equation of parabola.