Question

A diameter of a circle has endpoints P(-10,-2) and Q(4,6).

a. Find the center of the circle
b. Find the radius. If your answer is not an interger, express it in radical form.
c. Write and equation for the circle

Answer 1

The equation for the midpoint is given by:

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

`P = ((-10 + 4)/(2) , (-2 + 6)/(2))`

`P = ((-6)/(2) , (4)/(2))`

`P = (-3 , 2)`
We can find the radius of the circle using the equation of distance between points:

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

`d = √((4-(-3))^2 + (6-2)^2)`

`d = √((4+3)^2 + (4)^2)`

`d = √((7)^2 + (4)^2)`

`d = √(49 + 16)`

`d = √(65)`
The equation of the circle is its standard form is:

`(x-xo) ^ 2 + (y-yo) ^ 2 = r ^ 2`
Where,
(xo, yo): coordinates of the center of the circle
r: radius of the circle
Substituting values:

`(x + 3) ^ 2 + (y-2) ^ 2 = 65`