ANSWER
The required equation is,
[tex] {(x + 2)}^{2} + {(y + 7)}^{2} = 1296[/tex]
EXPLANATION
We want to find the equation of the circle given center [tex](-2,-7) [/tex]
and radius [tex]36[/tex] units.
The equation of a circle given the radius,
[tex]r[/tex]
and center
[tex](a,b) [/tex]
is given by the formula,
[tex] {(x - a)}^{2} + {(y - b)}^{2} = {r}^{2} [/tex]
We substitute,
[tex]a=-2,b=-7, r=36 [/tex]
to obtain,
[tex] {(x - - 2)}^{2} + {(y - - 7)}^{2} = {(36)}^{2} [/tex]
This will simplify to give us,
[tex] {(x + 2)}^{2} + {(y + 7)}^{2} = 1296[/tex]
The correct answer is D.
