jee-advanced 2010 Q36

jee-advanced · India · paper2 Circles Circle-Related Locus Problems
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.
The equation of the locus of the point whose distances from the point $P$ and the line AB are equal, is
A) $9 x ^ { 2 } + y ^ { 2 } - 6 x y - 54 x - 62 y + 241 = 0$
B) $x ^ { 2 } + 9 y ^ { 2 } + 6 x y - 54 x + 62 y - 241 = 0$
C) $9 x ^ { 2 } + 9 y ^ { 2 } - 6 x y - 54 x - 62 y - 241 = 0$
D) $x ^ { 2 } + y ^ { 2 } - 2 x y + 27 x + 31 y - 120 = 0$
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.

The equation of the locus of the point whose distances from the point $P$ and the line AB are equal, is\\
A) $9 x ^ { 2 } + y ^ { 2 } - 6 x y - 54 x - 62 y + 241 = 0$\\
B) $x ^ { 2 } + 9 y ^ { 2 } + 6 x y - 54 x + 62 y - 241 = 0$\\
C) $9 x ^ { 2 } + 9 y ^ { 2 } - 6 x y - 54 x - 62 y - 241 = 0$\\
D) $x ^ { 2 } + y ^ { 2 } - 2 x y + 27 x + 31 y - 120 = 0$