Answer:
Step-by-step explanation:
directrix is x=-4
or x+4=0
let (x,y) be any point on the parabola.
distance of (x,y) from (-1,15) is
[tex]=\sqrt{(x+1)^2+(y-15)^2}[/tex]
distance of (x,y) from x+4=0 is
[tex]=\frac{x+4}{\sqrt{1} } \\=(x+4)[/tex]
so
[tex]x+4=\sqrt{(x+1)^2+(y-15)^2} \\squaring\\x^{2} +8x+16=x^{2} +2x+1+(y-15)^2\\6x+15=(y-15)^2\\divide ~by~6\\x=\frac{1}{6} (y-15)^2-\frac{5}{2}[/tex]
