Tangents are drawn from the point to the ellipse

MATHEMATICS · Single correct · CBSE · Mathematics · Conic Sections · Conic Sections

Problem

Tangents are drawn from the point

P(3,4)

to the ellipse

\frac{x^2}{9}+\frac{y^2}{4}=1

, touching the ellipse at points

A

and

B

. Find the equation of the locus of a point whose distances from

P

and the line

AB

are equal. (1)

9x^2+y^2-6xy-54x-62y+241=0

(2)

x^2+9y^2+6xy-54x+62y-241=0

(3)

9x^2+9y^2-6xy-54x-62y-241=0

(4)

x^2+y^2-2xy+27x+31y-120=0