Question

The radius of circle $x^2-4x+y^2+6y=3$

• A. $3$
• B. $\sqrt{3}$
• C. $4$
• D. $8$
• E. $16$

Answer 1

Answer: (C)

$4$

The equation of a circle with center $(h,k)$ and radius $r$ is
$(x-h{)}^2+(y-k{)}^2=r^2$
To get our equation in this form and thus find the center and radius, we complete the square in both $x$ and $y$.
$\Rightarrow x^2-4x+y^2+6y=3$

$\Rightarrow (x+4x)+(y-6y)=3$
$\Rightarrow (x^2+4x+4)+(y^2-6y+9)=3+4+9$
$\Rightarrow (x+2{)}^2+(y-3{)}^2=16=4^2$
Hence, the radius of the given circle is $4$.