Q36 / 57 · JEE Advanced 2010 (Paper 2) · Mathematics
Paragraph:
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 $B$.Question:
The equation of the locus of the point whose distance from the point $P$ and the line $A B$ are equal, is
- Correct answerA$9 x^2+y^2-6 x y-54 x-62 y$ $$ +241=0 $$
- 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$x^2+y^2-2 x y+27 x+31 y$ $$ -120=0 $$
Solution
Equation of $A B$ is $y-0=-\frac{1}{3}(x-3)$
$$
\begin{gathered}
x+3 y-3=0 \\
|x+3 y-3|^2=10\left[(x-3)^2+(y-4)^2\right]
\end{gathered}
$$
(Look at coefficient of $x^2$ and $y^2$ in the
answers)
Hence, the correct answer is option: 'A'.