Question

Find the equation of the circle if one of the endpoints of the diameter is (-2,-3) and the midpoint of the circle's diameter is (4,5).

Answer 1

The answer to your question is (x - 4)² + (y - 5)² = 100

Explanation:

Data

Point = (-2, -3)

Midpoint = (4, 5)

Process

1.- Find the length of the radius using the formula of the distance between two points.

dPM =
`\sqrt{(x2 - x1)^(2)+ (y2 - y1)^(2)}`

x1 = -2 y1 = -3 x2 = 4 y2 = 5

dPM =
`\sqrt{(4 + 2)^(2) + (5 + 3)^(2)}`

dPM =
`\sqrt{(6)^(2) + (8)^(2)}`

dPM =
`√(36 + 64)`

dPM =
`√(100)`

dPM = 10

2.- Find the equation of the line

(x - h)² + (y - k)² = r²

h = 4

k = 5

r = 10

(x - 4)² + (y - 5)² = 10²

(x - 4)² + (y - 5)² = 100