The graph of the equation x^2+6x+y^2-16y=-9 is a circle. Choose True or False for each statement

A. The center of the circle is (3,-8). (true or false?)

B. The circle is tangent to the x-axis. (true or false?)

C. The circle has a radius of 64. (true or false?)

see the explanation

Step-by-step explanation:

we have

Convert the equation of the circle in center radius form

Group terms that contain the same variable

Complete the square twice. Remember to balance the equation by adding the same constants to each side

Rewrite as perfect squares

The center of the circle is (-3,8)

The radius of the circle is 8 units

Verify each statement

A. The center of the circle is (3,-8).

False

The center of the circle is (-3,8)

B. The circle is tangent to the x-axis

True

The circle is tangent to x=5 and x=-11 and is tangent to y=0 and y=16

Remember that y=0 is the x-axis

C. The circle has a radius of 64

False

The radius of the circle is 8 units

associative property of multiplication

use distributive property on all like terms and change your signs if you have a double negative or if you have positive/negative