Question

The center of a circle is at (−2, −7) and its radius is 6.

What is the equation of the circle?

Responses

(x+2)2+(y+7)2=3
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 3

(x+2)2+(y+7)2=36
open parenthesis x plus 2 close parenthesis squared plus open parenthesis y plus 7 close parenthesis squared equals 36

(x−2)2+(y−7)2=3
open parenthesis x minus 2 close parenthesis squared plus open parenthesis y minus 7 close parenthesis squared equals 3

(x−2)2+(y−7)2=36

Answer 1

option B is correct:
`(x+2)^2+(y+7)^2=36`

The general equation of the circle is given by:

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

where,

(h, k) is the center of the circle and r is the radius of the circle.

As per the statement:

The center of a circle is at (−2, −7) and its radius is 6.

`\implies (h, k) = (-2, -7)` and
`r = 6` units

Substitute these we have:

`(x-(-2))^2+(y-(-7))^2=6^2`

`\implies(x+2)^2+(y+7)^2=36`

Therefore, the equation of circle is,
`\bold{(x+2)^2+(y+7)^2=36}`