Question

If one of the diameters of the curve $x^2+y^2-4x-6y+9=0$ is a chord of a circle with centre $(1,1)$, the radius of this circle is

• A. $3$
• B. $2$
• C. $\sqrt{2}$
• D. $1$

Answer 1

The correct option is A $3$

centre of the circle $x^2+y^2-4x-6y+9=0$ is $(2,3)$
and radius of this circle is $\sqrt{4+9-9}=2\text{units}$

centre to centre distance between the circles $=\sqrt{(2-1{)}^2+(3-1{)}^2}=\sqrt{5}\text{units}$

$\therefore$ Radius of bigger circle $=\sqrt{2^2+(\sqrt{5}{)}^2}=3\text{units}$