Question

Let $L_1$ be a straight line passing through the origin and $L_2$ be the straight line x + y=1. If the intercepts made by the circles $x^2+y^2-x+3y=0$ on $L_1$ and $L_2$ are equal then which of the following equations can represent $L_1?$

• A. x+y=0
• B. x-y=0
• C. 7x-y=0
• D. x-7y=0

Answer 1

The correct option is B x-y=0

Length of the chord $=\sqrt{r^2-d^2}$

$=\sqrt{\frac{10}{4}-2}$

Let y = mx is chord through origin

$\therefore$ Length of chord
$\therefore \sqrt{2}=2\sqrt{\frac{10}{4}-{\left(\frac{\frac{m}{2}+\frac{3}{2}}{m^2+1}\right)}^2}$
$\Rightarrow (m+3{)}^2=8(m^2+1)\Rightarrow m=1,=-\frac{1}{7}$
$\therefore$ line equation is $y=x\left(or\right)7x+y=0$