Question

Please help. I am lost

Answer 1

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

$=\sqrt{(x+1)^2+(y-15)^2}$

distance of (x,y) from x+4=0 is

$=\frac{x+4}{\sqrt{1} } \\=(x+4)$

so

$x+4=\sqrt{(x+1)^2+(y-15)^2} \\squaring\\x^{2} +8x+16=x^{2} +2x+1+(y-15)^2\\6x+15=(y-15)^2\\divide ~by~6\\x=\frac{1}{6} (y-15)^2-\frac{5}{2}$