+16 The x intercepts of a circle are -3 and 10. One of the y intercepts is 5. What is the other y intercept? What is
the area of the circle?
+1926 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! :)
