Question

Given: circle O with diameter CD C(-5,4) D(3,-2) create a equation if the circle?

Answer 1

`(x+1)^2+(y-1)^2=25`

Explanation:

Mid point CD is the center:
The midpoint of a segment with endpoints A = (x₁, y₁) and B = (x₂, y₂) has coordinates :
[(x₁ + x₂) /2 , (y₁ + y₂)/2]
so in this case the center is:
`[(-5 + 3) /2 , (4 - 2)/2]` = `(-1, 1)`

Half of Length of CD is the radius:
distance 'd' between the points A = (x₁, y₁) and B = (x₂, y₂) is:
d = √[(x₂ - x₁)² + (y₂ - y₁)²]
so in this case:
`r = 1/2√[(3 + 5)^2 + (-2 - 4)^2]`
`r = 1/2 √[(8)^2 + (-6)^2]`
`r = 1/2√(64+36)=5`

The equation of the circle:
`(x+1)^2+(y-1)^2=25`