Question

The internal centre of similitude of two circles ${(x-3)}^2+{(y-2)}^2=9,{(x+5)}^2+{(y+6)}^2=9$ is:

• A. $(-1,-2)$
• B. $(-2,-1)$
• C. $(3,2)$
• D. $(-5,-6)$

Answer 1

The correct option is A $(-1,-2)$

$C1=(3,2),r1=3$

$C2=(-5,-6),r2=3$

Let P = Internal center of similitude, it divides C1C2 in the ratio r1 : r2 internally

$P=\frac{3C_2+3C_1}{3+3}=(\frac{-15+9}{6},\frac{-18+6}{6})=(-1,-2)$