What is the radius of a circle of the function x^2+y^2+2x-6y=10 at the center (-1,3).

In a circle with the equation of the
form:

x^2 + y^2 - 2ax - 2by + c =
0

The center of the circle is given by (a,
b).

and radius of the circle is given
by:

Radius = (c - a^2 -
b^2)^(1/2)

The given equation
is:

x^2 + y^2 + 2x - 6y + 10 =
0

Therefore:

a = -1, b = 3,
and c = 10

This center of the circle is (-1,
3).

As we can see this is same as the center given in the
question.

Radius = (c - a^2 -
b^2)^(1/2)

= [10 + (-1)^2 +
3^2]^1/2

= (10 + 1 + 9)^1/2 = 20^1/2 =
4.4721

Please note that we could have calculated the length
of the radius even if the center of the circle was not given.