Question

Find the center and radius of the given circle and graph it.

15. x^2+y^2+10y+21=0

Answer 1

$\mathrm{x}^{\wedge}2 + \mathrm{y}^{\wedge}2 + 10\mathrm{y} + 21 = 0;$
$\mathrm{x}^{\wedge}2 + \mathrm{y}^{\wedge}2 + 10\mathrm{y} + 21 + 4 - 4 = 0;$
$\mathrm{x}^{\wedge}2 + (\mathrm{y}^{\wedge}2 + 10\mathrm{y} + 25) = 4;$
$\mathrm{x}^{\wedge}2 + (\mathrm{y} + 5)^{\wedge}2 = 2^{\wedge}2;$
(x-a)^2+(y-b)^2=R^2 - equation of a circle, where (a,b) - center and R is a radius of a circle.
(x-0)^2+(y-(-5))^2=2^2;
So, point (0,-5) - center of a circle and R=2 - radius of a circle;