8.5 Equation of a Circle

Unit 8: Circles

8.5 Equation of a Circle

Match

Complete the formulas by matching.

• $$2\pi r$$

• $$\pi r^2$$

• $$\pi d$$

• $$\frac{x\cdot C}{360}$$

• $$\frac{x\cdot2\pi r}{360}$$

=Circumference using radius

=Area of a circle

=Circumference using diameter

=Arc length using circumference

=Arc length using radius

• =Circumference using radius

• =Area of a circle

• =Circumference using diameter

• =Arc length using circumference

• =Arc length using radius

Multiple Choice

Find the length of the bold arc.Leave pi in your answer.

• 5688π ft

• 15.8π ft

• 150.4π ft

• 54,150 ft

1.Equation of a Circle Formula

Example 1:

​Write the equation of the circle with the center point (5,3) and the a radius of 2.

Example 2:

​Write the equation of the circle with the center point (-1,7) and the a radius of 14.

Math Response

Write the equation of the circle with a center at (-2, -11) and a radius 8.

Type answer here

Correct Answer: \left(x+2\right)^2+\left(y+11\right)^2=8^2

Deg^°

Rad

Math Response

Write the equation of the circle with a center at (0, 9) and a radius 32.

Type answer here

Correct Answer: \left(x+0\right)^2+\left(y-9\right)^2=32^2

Deg^°

Rad

Math Response

Write the equation of the circle with a center at (-4,0) and a radius $$\sqrt[]{47}$$ .

Type answer here

Correct Answer: \left(x+4\right)^2+\left(y+0\right)^2=\sqrt{47}^2

Deg^°

Rad

Math Response

Write the equation of the circle with a center at (15,-6) and a radius $$\sqrt[]{158}$$ .

Type answer here

Correct Answer: \left(x-15\right)^2+\left(y+6\right)^2=\sqrt{158}^2

Deg^°

Rad

Dropdown

If the equation of the circle is $$\left(x-5\right)^2+\left(y-1\right)^2=64$$ ​ then the center is ​ ​

Select answer

and r=​

Select answer

Dropdown

If the equation of the circle is $$\left(x-6\right)^2+\left(y+11\right)^2=58$$ , then the center point is ​

Select answer

and the radius is ​

Select answer

Multiple Choice

Write the equation of the circle.

• (x+1)² + (y +1)² = 3

• (x+1)² + (y -1)² = 3

• (x+1)² + (y +1)² = 9

• (x-1)² + (y -1)² = 9

Multiple Choice

What is the equation for this circle?

• (x+1)+(y+1)=9

• x²+y²=9

• x+y=9