Question

Find the standard form for the equation of a circle ( x − h ) 2 + ( y − k ) 2 = r 2 with a diameter that has endpoints ( − 7 , 4 ) and ( 5 , − 5 ) .

Answer 1

(X+1)^2 + (y+1/2)^2 = 225/4

Explanation:

Center= (-7+5) /2 = - 2/2 = -1 and (4-5)/2 = - 1/2

Coordinates of the center = (-1, - 1/2 )

(-1 is the h coordinate in the circle equation and -1/2 is the k)

Distance of the diameter= sqrt [(-7- 5)^2 + (4 - - 5)^2]

d = sqrt [(-12)^2 + (9)^2

d = sqrt (144+81)

d = sqrt 225

( the value of the radius in the equation is squared so the radius is (sqrt 225/2)^2=

Radius= 225/4

The equation of circle is: (x - - 1)^2 + (y - - 1/2) = 225/4