Question

A circle has a diameter with endpoints

C(20, -21) and D(-20, 21). Determine the equation of the circle.

Answer 1

x² + y² = 841

Explanation:

Midpoint of diameter is a center of a circle.

Coordinates of midpoint are

(
`x_(1)` ,
`y_(1)` )

(
`x_(2)` ,
`y_(2)` )

(
`(x_(1) +x_(2) )/(2)` ,
`(y_(1) +y_(2) )/(2)` )

d =
`\sqrt{(x_(2) -x_(1))^2 +(y_(2) -y_(1))^2 }`

Equation of a circle with center at (h, k) and radius "r" is (x - h)² + (y - k)² = r²

~~~~~~~~~~

C(20, 21)

D(- 20, 21)

(
`(-20+20)/(2)` ,
`(-21+21)/(2)` ) = (0, 0)

d =
`√((-20-20)^2 +(21+21)^2)` = √3364 = 58

r =
`(d)/(2)` = 29

x² + y² = 29²

x² + y² = 841