Question

The equation of the line passing through the centre and bisecting the chord $7x+y-1=0$ of the ellipse $\frac{x^2}{1}+\frac{y^2}{7}=1$ is

• A. $x=y$
• B. $2x=y$
• C. $x=2y$
• D. $x+y=0$

Answer 1

Answer: (A)

$x=y$

Let $(h,k)$ be the midpoint of the chord $7x+y-1=0$
$\Rightarrow \frac{hx}{1}+\frac{ky}{7}=\frac{h^2}{1}+\frac{k^2}{7}$ (i)
and $7x+y=1$ (ii)
represents same straight line
$\Rightarrow \frac{h}{7}=\frac{k}{7}\Rightarrow h=k$
$\Rightarrow$ Equation of the line joining $(0,0)$ and $(h,k)$ is $y-x=0$.
Hence, option 'A' is correct.