Find an equation of the circle that satisfies the stated cor Endpoints of a diameter A(2, - 9) and B(- 6, 7)

Question

Find an equation of the circle that satisfies the stated cor Endpoints of a diameter A(2, - 9) and B(- 6, 7)

Answer 1

Per distance formula, The diameter is

sqrt ( (2 - -6)^2 + (-9 - 7)^2) =

sqrt ( 8^2 + (-16)^2) =

sqrt ( 64 + 256) =

sqrt(320) =

sqrt(64*5)=

8*sqrt(5)

THe radius is then R=4*sqrt(5) ---> R^2 = 80

Per midpoint formula, the center is at

(2 + -6)/2 , (-9 + 7)/2

-4/2 , -2/2

(-2,-1)

The equation of the circle is then

(x+2)^2 + (y+1)^2 = 80