Question

Equation of the chord of contact of pair of tangents drawn to the ellipse $4x^2+9y^2=36$ from the point $(m,n)$ where $m.n=m+n;m,n$ being non-zero positive integers is

• A. $2x+9y=18$
• B. $2x+2y=1$
• C. $4x+9y=18$
• D. None of these

Answer 1

Answer: (C)

$4x+9y=18$

Given $m(n-1)=n$
$n$ is divisible by $n-1$
$\Rightarrow n=2\Rightarrow m=2$
Hence, chord of contact of tangents drawn from $(2,2)$ to
$\frac{x^2}{9}+\frac{y^2}{4}=1$ is $\frac{2x}{9}+\frac{2y}{4}=1$
$\Rightarrow 4x+9y=18$