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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?

 Jun 11, 2024
 #1
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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! :)

 Jun 11, 2024

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