Question

The internal centre of similitude of the circles $x^2+y^2-2x+4y+4=0$ and
$x^2+y^2+4x-2y+1=0$ is

• A. $(0,1)$
• B. $(-1,0)$
• C. $(0,-1)$
• D. $(1,-1)$

Answer 1

The correct option is C $(0,-1)$

From Point (11)
$S_1:x^2+y^2-2x+4y+4=0$
$C_1\equiv (1,-2)$ and $r_1=1$
$S_2:x^2+y^{2}4x-2y+1=0$
$C_2\equiv (-2,1)$ and $r_2=2$
$\therefore \frac{r_1=1r_2=2}{C_1(1,-2)p(x,y)}{C}_2(-2,1)$
$x=\frac{-2+2}{1+2}$ & $y\frac{1\times 1+2(-2)}{1+2}$
$x=0$ & $y=\frac{-3}{3}=-1$
$(0,-1)$ is internal centre of similitude of the circles $S_1$ and $S_2$.