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What is the diameter of a circle with the equation (x + 6)2 + (y − 4)2 = 16?

A) 4
B) 8
C) 16
D) 32

User Rossitten
by
8.1k points

1 Answer

1 vote

The diameter of the circle is 8, which is mentioned in option B, if a circle equation is
(x+6)^(2)+(y-4)^(2) = 16.

Explanation:

The given is,

Circle equation is
(x+6)^(2)+(y-4)^(2) = 16.

Step:1

Equation for circle is,


(x-h)^(2)+(y-k)^(2) = r^(2).......................(1)

Where,

(h, k) - Center point

r - Radius of circle

Given equation,


(x-h)^(2)+(y-k)^(2) = r^(2)....................(2)

Comparing equation (1) and equation (2)

(h, k) - (-6, 4)


r^(2) - 16

Take square root on both side,


r = √(16)

r = 4

Formula for diameter,


d = 2r


=(2)(4)

= 8

Diameter of circle, d = 8

Result:

The diameter of the circle is 8, which is mentioned in option B, if a circle equation is
(x+6)^(2)+(y-4)^(2) = 16.

User Lady
by
8.4k points

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