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 $2\sqrt{2}cos45^o=2$
$\Rightarrow a=4$ or $-4$