how?

We can find the diameter of the circle with the 3 x intercepts. 

 

The diameter of a circle is the distance between any two points that crosses the center. Since the x intercepts defintely cross the center, the diamter is

\(10-(-3)=13\)

 

Now, the same goes for the y intercept. Since the other y intercept must be 13 units away from 5, then we have \(5-13=-8\)

 

So the other y intercept is -8. 

 

Now, for the area, we already know the diameter, and the radius is half the diameter, so we have \(r=\frac{1}{2}13 = 6.5\)

 

The area of the circle is equal to \(r^2 \pi\), so plugging in 6.5, we get \(42.25\pi\) as the area. 

 

Thanks! :)