Writing Equations of Circles Using the Pythagorean Theorem

What is the equation of a circle centered at the origin?

• x^2 + y^2 = r^2

• x + y = r

• x^2 + y^2 = 2r

• x^2 - y^2 = r^2

When a circle is moved from the origin, what do the variables h and k represent?

• The distance from the origin

• The lengths of the legs of a triangle

• The coordinates of the center

• The radius of the circle

How do you find the horizontal leg length when the circle is centered at (h, k)?

• Subtract y from k

• Subtract h from x

• Add h to x

• Multiply x by h

What is the general equation of a circle centered at (h, k)?

• x^2 + y^2 = r^2

• x - h + y - k = r

• x - h)^2 + (y - k)^2 = r^2

• x + h)^2 + (y + k)^2 = r^2

If a circle is centered at (3, 2) with a radius of 8, what is its equation?

• (x + 3)^2 + (y + 2)^2 = 8

• (x - 3)^2 + (y - 2)^2 = 8

• (x - 3)^2 + (y - 2)^2 = 64

• (x + 3)^2 + (y + 2)^2 = 64

What is the equation of a circle centered at (-5, 1) with a radius of 6?

• (x - 5)^2 + (y + 1)^2 = 36

• (x + 5)^2 + (y + 1)^2 = 6

• (x - 5)^2 + (y - 1)^2 = 6

• (x + 5)^2 + (y - 1)^2 = 36

What is the first step in writing the equation of a circle given its center and radius?

• Identify the radius

• Identify the center coordinates

• Subtract the center coordinates from x and y

• Multiply the radius by 2