ANSWER
[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]
EXPLANATION
The equation of the circle in general form is given as:
[tex] {x}^{2} + {y}^{2} + 20x + 12y + 15 = 0[/tex]
To obtain the standard form, we need to complete the squares.
We rearrange the terms to obtain:
[tex] {x}^{2} + 20x + {y}^{2} + 12y = - 15 [/tex]
Add the square of half the coefficient of the linear terms to both sides to get:
[tex]{x}^{2} + 20x +100 + {y}^{2} + 12y + 36 = - 15 + 100 + 36[/tex]
Factor the perfect square trinomial and simplify the RHS.
[tex]{(x + 10)}^{2} + {(y + 6)}^{2} = 121[/tex]
This is the equation of the circle in standard form.
