Question

Let $PQ$ be the common chord of the circles $S_1:x^2+y^2+2x+3y+1=0$ and $S_2:x^2+y^2+4x+3y+2=0$ , then the perimeter (in units) of the triangle $C_{1}PQ$ is equal to $($ where,$C_1=\left(-1,\frac{-3}{2}\right))$

• A. $\frac{9}{2}$
• B. $2\sqrt{2}+3$
• C. $3\sqrt{2}+2$
• D. $\frac{3}{2}+2\sqrt{2}$

Answer 1

Answer: (B)

Equation of the common chord is $2x+1=0$

$C_{1}M=\left|\frac{-2+1}{2}\right|=\frac{1}{2}$
$PM=\sqrt{\frac{9}{4}-\frac{1}{4}}=\sqrt{2}$
Length of the common chord $=2\sqrt{2}$
Hence, the perimeter of $\Delta C_{1}PQ=\frac{3}{2}+\frac{3}{2}+2\sqrt{2}$
$=3+2\sqrt{2}$ units