Question

The coordinates of the radical centre of three circles $x^2+y^2+2x+3y+1=0,x^2+y^2+x+y+2=0,x^2+y^2+3x+2y+1=0$

• A. $\left(6,30\right)$
• B. $\left(\frac{1}{3},\frac{1}{3}\right)$
• C. $\left(3,0\right)$
• D. None of these

Answer 1

The correct option is B $\left(\frac{1}{3},\frac{1}{3}\right)$

$S_1:x^2+y^2+2x+3y+1=0$

$S_2:x^2+y^2+x+y+2=0$

$S_3:x^2+y^2+3x+2y+1=0$

Radius axis of $S_1$ & $S_2$

$L_1:S_1-S_2=0\to x+2y-1=0$

Radical axis of $S_2$ & $S_3$

$L_2:S_2-S_3=0\to -2x-y+1=0$

Intersection of $L_1$ & $L_2$ is radical centre.

Radical centre is $(\frac{1}{3},\frac{1}{3})$

$B$ is correct