Question

Equation of the chord of contact, drawn to the ellipse $4x^2+9y^2=36$ from the point $(m,n)$ where $m\cdot n=m+n$ and $m,n\in I^{+}$ is

• A. $4x+9y=9$
• B. $2x+2y=1$
• C. $4x+9y=18$
• D. $4x+9y=36$

Answer 1

The correct option is C $4x+9y=18$

Given that $m\cdot n=m+n$
$\Rightarrow m(n-1)=n$
$\Rightarrow m=\frac{n}{n-1}$
As given that $n,m$ are integres. So, in above equation for being $m$ an integer $n$ must be divisible by $n-1$ that is possible only when $n=2$
$\therefore n=2\Rightarrow m=2$
Hence, chord of contact drawn from$(2,2)$ to $\frac{x^2}{9}+\frac{y^2}{4}=1$ is,
$\Rightarrow \frac{2x}{9}+\frac{2y}{4}=1$
$\Rightarrow 4x+9y=18$