Question

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

Answer 1

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`.