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A circle has a diameter with endpoints

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

1 Answer

12 votes

Answer:

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

User Dipanjan Mallick
by
6.9k points
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