Ellipse 3 Question 1
1. The equation of the locus of the point whose distance from the point $P$ and the line $A B$ 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) $x^{2}+y^{2}-2 x y+27 x+31 y-120=0$
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Answer:
Correct Answer: 1. (a)
Solution:
- Equation of $A B$ is $y-0=-\frac{1}{3}(x-3)$
$$ \begin{array}{rlrl} & x+3 y-3 & =0 \\ \Rightarrow & & |x+3 y-3|^{2} & =10\left[(x-3)^{2}+(y-4)^{2}\right] \end{array} $$
On solving, we are getting
$$ 9 x^{2}+y^{2}-6 x y-54 x-62 y+241=0 $$
