Question

The possible number of values of $a$ for which the common chord of the circles $x^{2}+y^{2}=8$ and $\left(x - a\right)^{2}+y^{2}=8$ subtends a right angle at the origin is

• A. $0$
• B. $2$
• C. $5$
• D. $3$

Answer 1

Answer: (B)

Equation of the common chord is $\left(x - a\right)^{2}+y^{2}-8-x^{2}-y^{2}+8=0$
$\Rightarrow -2ax+a^{2}=0\Rightarrow x=\frac{a}{2}$
If the chord $x=\frac{a}{2}$ subtends a right angle at $\left(0,0\right)$ then the distance of $x=\frac{a}{2}$ from the origin is equal to $2\sqrt{2}cos 45^{o}=2$
$\Rightarrow a=4$ or $-4$