Question

The area of the circle represented by the equation ${(x+3)}^2+{(y+1)}^2=25$ is

• A. $4\pi$
• B. $5\pi$
• C. $16\pi$
• D. $25\pi$

Answer 1

Answer: (D)

$25\pi$

The general equation of circle with centre $(h,k)$ and radius $r$ is given by ${(x-h)}^2+{(y-k)}^2={\left(r\right)}^2$.

It is given that the equation of the circle is $(x+3{)}^2+(y+1{)}^2=25$

Therefore, $h=-3$, $k=-1$ and $r=5$.

The area of the circle with radius $r$ is $\pi r^2$, thus the area of the circle with radius $r=5$ is:

$\pi r^2=\pi {\left(5\right)}^2=25\pi$

Hence, the area of the circle is $25\pi$.