Explanation:

Focus is(-6,-6)

Vertex is (-1,2)

Directrix and x axis bisects point

Let (a,b)

-1=(-6+a)  /2

-2  =-6 +a

a=4

2  =(-6 +b)/2

4  =-6+b

b=10

directrix equation is

y-10=m(x-4)

gradient m=10-(-6)/4-(-6)

=16/10

=8/5

y-10  =8/5 (x-4)

5y -50 =8x-32

5y-8x=18

Let  P (x,y) is the point on parabola

PM is perpendicular on the directrix

Equation of parabola is

√((x+6)²  +(y+6)² )  =5y-8x -18/√(25+64)

((x+6)²  +(y+6)² )  =(5y-8x-18)²/89

(x+6)² +(y+6)²   =25y²  +64x² -80xy

89X²+36×89+12x(89)+89y²+36×89+12y(89)=25y²+64x²-80xy

25x² +4272+64y²  +3204+1068y+80xy  =0