## Problem 1117

Find the center and radius of the circle. Then graph the circle.

x^{2} + y^{2} + 3x – 5y – = 0

**Solution:-**

To find the center and the radius, complete the square and then write the equation in standard form.

(x – h)^{2} + (y – k)^{2} = r

Regroup the terms.

(x^{2} + 3x ) + (y^{2} – 5y) =

First complete the square, add to both sides of the equation.

(x^{2} + 3x + ) + (y^{2} -5y) =

Now complete square for y^{2} – 5y.

To complete the square, add to both sides of the equation.

(x + 3x + ) + (y – 5y + )

=

Simplify the right-hand side.

(x + 3x + ) + (y – 5y + )=

Now write the equation in standard form.

(x – h)^{2} + (y – k)^{2} = r^{2}

h = –

k =

The radius is .

To sum up, the center is () and the radius is .

To graph the circle, first plot the center (-).

To complete the circle, use the radius to find all the points equidistant from the center.