Question 874597
Q:
A circle is described by the equation {{{x^2 + y^2 + 14x + 2y + 14 = 0}}}. What are the coordinates for the center of the circle and the length of the radius?
A:
Express the equation in the form {{{(x - h)^2 + (y - k)^2 = r^2}}}.
{{{x^2 + y^2 + 14x + 2y + 14 = 0}}}
{{{(x^2  + 14x) + (y^2 + 2y) = -14}}}
{{{(x^2  + 14x + 49) + (y^2 + 2y + 1) = -14 + 49 + 1}}}
{{{(x + 7)^2 + (y + 1)^2 = 36}}}
h = -7, k = -1, and r = {{{sqrt(36)}}} = 6
Therefore, the center is (-7, -1) and the length of the radius is 6.