Question

The equation of a circle in general form is ​ x2+y2+20x+12y+15=0 ​ . What is the equation of the circle in standard form?

Answer 1

Answer:

(x)²+(y)²=0

Step-by-step explanation:

Answer 2

ANSWER

${(x + 10)}^{2} + {(y + 6)}^{2} = 121$

EXPLANATION

The equation of the circle in general form is given as:

${x}^{2} + {y}^{2} + 20x + 12y + 15 = 0$

To obtain the standard form, we need to complete the squares.

We rearrange the terms to obtain:

${x}^{2} + 20x + {y}^{2} + 12y = - 15$

Add the square of half the coefficient of the linear terms to both sides to get:

${x}^{2} + 20x +100 + {y}^{2} + 12y + 36 = - 15 + 100 + 36$

Factor the perfect square trinomial and simplify the RHS.

${(x + 10)}^{2} + {(y + 6)}^{2} = 121$

This is the equation of the circle in standard form.