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JEE Advanced 2010Paper 2

Exam: JEE Advanced
Year: 2010
Paper: Paper 2
Subject: Mathematics
Chapter: Ellipse

JEE Advanced 2010 · Paper 2 · Mathematics · Ellipse

Paragraph: Tangents are drawn from the point P(3,4) to the ellipse...

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

Options

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

Correct answer

A. $9 x^2+y^2-6 x y-54 x-62 y$ $+241=0$

Step-by-step 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)

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