Question

Given $c_1:x^2+y^2-2x-2y+3=0$ and $c_2:2x^2+2y^2-4x-4y+7=0$ are

• A. concentric circles
• B. similar circles
• C. congruent circles
• D. none of these

Answer 1

The correct option is A concentric circles

Center of a circle is given by the equation

$a{x}^2+a{y}^2+2gx+2fy+c=0$ as $(\frac{-g}{a},\frac{-f}{a})$

Center of $C_1=(\frac{1}{1},\frac{1}{1})=(1,1)$

Center of $C_2=(\frac{2}{2},\frac{2}{2})=(1,1)$

C1 and C2 have the same center

C1 and C2 are concentric