Question

The radius of the circle $x^2+y^2+2x+8y+8=0$ is

• A. $5\text{units}$
• B. $4\text{units}$
• C. $3\text{units}$
• D. $8\text{units}$

Answer 1

Answer: (C)

Given:

Equation of the circle is $x^2+y^2+2x+8y+8=0$

We know that, the general form of the circle is $a{x}^2+b{y}^2+2gx+2fy+c=0,a,b\ne 0$
Comparing with the general form of circle equation, we get

$a=1,b=1$ and

$2g=2\Rightarrow g=1$

$2f=8\Rightarrow f=4$

$c=8$
Centre $(-g,-f)=(-1,-4)$

Radius, $r=\sqrt{g^2+f^2-c}$

$\Rightarrow$ Radius of the circle $\left(r\right)=\sqrt{g^2+f^2-c}$

$\Rightarrow r=\sqrt{(-4{)}^2+(-1{)}^2-8}$

$\Rightarrow r=\sqrt{16+1-8}$

$\Rightarrow r=\sqrt{9}$

$\Rightarrow r=3$

Hence, Option C is correct.