Question

If focus of parabola is F (2, 5) and equation of directrix is x + y=2, then find the equation of parabola.

(a) x^2+y^2+2xy-4x-16y+54=0

(b) x^2+y^2+2xy+4x-16y+54=0

(c) x^2+y^2+2xy+4x+16y+54=0

(d) x^2+y^2+2xy-4x+16y+54=0

I had been asked this question at a job interview.

Question is taken from Conic Sections in portion Conic Sections of Mathematics – Class 11

Answer 1

The correct choice is (a) x^2+y^2+2xy-4x-16y+54=0

Explanation: We know, if P is a point on parabola, M is foot of perpendicular drawn from point P to directrix of parabola and F is focus of parabola then PF=PM

(x-2)^2+(y-5)^2 = (|x+y-2|/√2)^2

x^2+y^2+2xy-4x-16y+54=0.