Question

Determine the equation of the parabola with focus (-4,5) and directrix x=16.

Answer 1

parabola is the locus of apoint which is equidistant from focus and directrix.
eq. of directrix is x=16
or x-16=0
let P(x,y) be any point on the parabola.
Let M be foot of perpendicular from P.
focus is F(-4,5)
PM=PF
\[\frac{ x-16 }{ \sqrt{1^2} }=\sqrt{(x+4)^2+(y-5)^2}\]
squaring
\[(x-16)^2=(x+4)^2+(y-5)^2\]
solve

Answer 2

we just need to find x and y correct? or am i thinking wrong