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=0I had been asked this question at a job interview.Question is taken from Conic Sections in portion Conic Sections of Mathematics – Class 11

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

1.	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=0I had been asked this question at a job interview.Question is taken from Conic Sections in portion Conic Sections of Mathematics – Class 11
Answer» 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.

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