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sveta [45]
3 years ago
10

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

Mathematics
1 answer:
BigorU [14]3 years ago
7 0

Answer:

see the explanation

Step-by-step explanation:

we have

x^2+6x+y^2-16y=-9

<u><em>Convert the equation of the circle in center radius form</em></u>

Group terms that contain the same variable

(x^2+6x)+(y^2-16y)=-9

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

(x^2+6x+9)+(y^2-16y+64)=-9+9+64

(x^2+6x+9)+(y^2-16y+64)=64

Rewrite as perfect squares

(x+3)^2+(y-8)^2=8^2

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

The radius of the circle is 8 units

<u><em>Verify each statement</em></u>

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

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