Question

what is the center?
the circle passes through the point (-7,-7). what is the radius?​

Answer 1

We have been given image of circle that passes through point $(-7,-7)$. We are asked to find the radius of the circle.

First of all, we will find the center of the circle.

We can see that center of circle is at point $(-2,-1)$.

Now we will use equation of circle to find radius.

$(x-h)^2+(y-k)^2=r^2$, where, point (h,k) represents center of circle and r represents radius of circle.

Now we will substitute the coordinates of point $(-7,-7)$ and coordinates of center $(-2,-1)$ and solve for r as:

$(-7+2)^2+(-7+1)^2=r^2$

$(-5)^2+(-6)^2=r^2$

$25+36=r^2$

$61=r^2$

Switch sides:

$r^2=61$

Now we will take positive square root on both sides:

$\sqrt{r^2}=\sqrt{61}$

$r=\sqrt{61}$

Therefore, radius of circle will be $\sqrt{61}$ and center is at point $(-2,-1)$.