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

Answer:

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

Step-by-step 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 = $\sqrt{36 + 64}$

dPM = $\sqrt{100}$

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