Question bank / Circles

Math · Geometry and TrigonometryMedium

In the xyxy-plane, a circle has center (−2,5)(-2, 5) and passes through the point (4,−3)(4, -3). Which of the following is an equation of the circle?

A

(x−2)2+(y+5)2=100(x - 2)^2 + (y + 5)^2 = 100

B

(x+2)2+(y−5)2=10(x + 2)^2 + (y - 5)^2 = 10

C

(x+2)2+(y−5)2=100(x + 2)^2 + (y - 5)^2 = 100

D

(x−4)2+(y+3)2=100(x - 4)^2 + (y + 3)^2 = 100

Show answer and explanation

Answer: C

The radius is the distance from the center to the given point: r2=(4−(−2))2+(−3−5)2=36+64=100r^2 = (4 - (-2))^2 + (-3 - 5)^2 = 36 + 64 = 100. With center (−2,5)(-2, 5), the equation is (x+2)2+(y−5)2=100(x + 2)^2 + (y - 5)^2 = 100.

Choice B sets the right side equal to the radius, 1010, instead of the radius squared.

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