Question

The diameter of a circle has endpoints of (2, 5) and (-4, 13). What is the correct equation of this circle? Pls explain and I will mark brainliest!

Answer 1

Answer:

• Option 4

Step-by-step explanation:

Midpoint of the diameter is the center.

Use midpoint formula to determine the coordinates:

• x = (2 - 4)/2 = -1
• y = (5 + 13)/2 = 9

Find the radius using the midpoint and one of the endpoints and the distance formula:

• r = $\sqrt{(-1 - 2)^2 + (9 - 5)^2} = \sqrt{9+16} = \sqrt{25} = 5$

Use the equation of the circle:

• (x - (-1))² + (y - 9)² = 5²
• (x + 1)² + (y - 9)² = 25

Correct choice is 4