Question bank / Circles

Math · Geometry and TrigonometryMedium

Which of the following is an equation of the circle in the xyxy-plane with center (0,−4)(0, -4) and radius 7\sqrt{7}?

A

x2+(y+4)2=7x^2 + (y + 4)^2 = 7

B

x2+(y−4)2=7x^2 + (y - 4)^2 = 7

C

x2+(y+4)2=49x^2 + (y + 4)^2 = 49

D

(x+4)2+y2=7(x + 4)^2 + y^2 = 7

Show answer and explanation

Answer: A

A circle with center (h,k)(h, k) and radius rr has equation (x−h)2+(y−k)2=r2(x - h)^2 + (y - k)^2 = r^2. With h=0h = 0, k=−4k = -4, and r2=(7)2=7r^2 = (\sqrt{7})^2 = 7, the equation is x2+(y+4)2=7x^2 + (y + 4)^2 = 7.

Choice B has the sign of the yy-coordinate reversed; (y−k)(y - k) with k=−4k = -4 becomes (y+4)(y + 4).

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