Question

The radius of the circle $x^2+y^2+4x+6y+13=0$is

• A. $\sqrt{26}$
• B. $\sqrt{13}$
• C. $\sqrt{23}$
• D. $0$

Answer 1

The correct option is D

$0$

The explanation for the correct answer.

Solve for the radius of the circle $x^2+y^2+4x+6y+13=0$

$x^2+y^2+4x+6y+13=0$

$$\begin{gathered} \Rightarrow (x^2+4x+4)+(y^2+6y+9)+13=4+9 \\ \Rightarrow {(x+2)}^2+{(y+3)}^2=0 \end{gathered}$$

Comparing it with the general equation of the circle,${(x-h)}^2+{(y-k)}^2=r^2$

where $(h,k)=$the center of circle and $r=$radius of the circle

$\therefore$ Radius of circle$=0$

Hence, option(D) is the correct answer.