Question

Tangents are drawn from the point P(3, 4) to the ellipse x²/9+y²/4 =1  touching the ellipse at point A and B. The equation of the locus of the point whose distances from the point P and the line AB are equal is

(A) 9x²+y²-6xy-54x-62y+241=0

(B) x²+9y²+6xy-54x+62y-241=0

(C) 9x²+9y²-6xy-54x-62y-241=0

(D) x² +y² -2xy -27x +31y-120=0

Answer 1

Correct option (A) 9x²+y²-6xy-54x-62y+241=0

Explanation:

Write the equation of the chord of contact w.r.t. point P. Then follow the standard procedure to find the locus. 

AB being the chord of contact of the ellipse from P(3, 4) has its equation

If (h, k) is any point on the locus, then