Question

What is the diameter of a circle with the equation (x – 4)2 + (y + 6)2 = 64?

a. 4
b. 8
c. 16
d. 64

Answer 1

They are correct. The answer is c. 16

Explanation:

Answer 2

The diameter of a circle with the equation is 16.

Explanation:

Given the equation

`\left(x\:-\:4\right)^2\:+\:\left(y\:+\:6\right)^2=\:64`

We know that the circle equation with radius 'r', centered at (a, b)

`\left(x-a\right)^2+\left(y-b\right)^2=r^2`

`\mathrm{Rewrite}\:\left(x-4\right)^2+\left(y+6\right)^2=64\:\mathrm{in\:the\:form\:of\:the\:standard\:circle\:equation}`

`\left(x-4\right)^2+\left(y-\left(-6\right)\right)^2=8^2`

Here,

radius = r = 8

center = (4, -6)

Hence, the radius of the circle is: r = 8

we know that

diameter = 2r

= 2(8)

= 16

Therefore, the diameter of a circle with the equation is 16.