Checkpoint: Equations of Circles Solution

Determine the equation of the circle with endpoints of the diameter being $(- 5, - 7)$ and $(- 5, - 11)$ .

$(\frac{- 5 + - 5}{2}, \frac{- 7 + - 11}{2}) Center : (- 5, - 9) r = \sqrt{{(- 5 + 5)}^{2} + {(- 9 + 11)}^{2}} r = 2 {(x + 5)}^{2} + (y + 9) = 2^{2} {(x + 5)}^{2} + {(y + 9)}^{2} = 4$

Note

Q: Do the given points represent a horizontal or vertical diameter on the circle? Explain.

A: This is a vertical diameter because the x-values are the same.

Q: What is the interval range of the circle?

A: Values including and between –7 and –11.