Question

A diameter of a circle has endpoints A (-6, -8) and B (2, 10).

Find the center of the circle.
Find the radius. If your answer is not an integer, express it in radical form.
Write an equation for the circle.

Answer 1

The first thing we must do for this case is to use the formula of the midpoint to find the center of the circle.
We have then:

`C = ( (x1 + x2)/(2) , (y1 + y2)/(2))`
Substituting values we have:

`C = ( (-6 + 2)/(2) , (-8 + 10)/(2))`

`C = ( (-4)/(2) , (2)/(2))`

`C = (-2, 1)`
We are now looking for the radius of the circle. For this, we use the formula of distance between points.
We have then:

`r = √((x2-x1)^2 + (y2-y1)^2)`
Substituting values we have:

`r = √((2-(-2))^2 + (10-1)^2)`

`r = √((4)^2 + (9)^2)`

`r = √(16 + 81)`

`r = √(97)`
We now write the standard equation of the circle:

`(x-xo)^2 + (y-yo)^2 = r^2`
Substituting values we have:

`(x+2)^2 + (y-1)^2 = 97`