Geometry Equations of Circles

Equations of Circles

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From the Equation

• Make the signs on h and k OPPOSITE to get the center

• Take the SQUARE ROOT of r² to get the radius

• If you don't SEE a h or k, then that means the coordinate is ZERO.

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the center of the circle is...

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

Multiple Choice

In the equation (x-3)²+(y-2)²=16, the radius of the circle is...

• 16

• 32

• 8

• 4

Multiple Choice

In the equation x²+(y+5)²=10, what is the center?

• (1, 5)

• (-1, -5)

• (0, 5)

• (0, -5)

To Write the Equation

• Make the signs on the center OPPOSITE before you plug them in for h and k.

• SQUARE the radius (multiply it by itself) before you plug it in for r²

• If you were given the diameter, then divide that by 2 to get the radius. And then square it before you plug it in as r²

Multiple Choice

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9

• x² + (y -7)² = 9

• (x - 7)² + y² = 3

• x² + (y -7)² = 3

Multiple Choice

Write the equation of a circle with center (0, 1) with radius 2.

• x² + (y - 1)² = 2

• x² + (y - 1)² = 4

• (x - 1)² + y² = 4

• x² + (y + 1)² = 4

Multiple Choice

The diameter of a circle has length 16. The center is at (0,0). Give the equation of the circle.

• x² + y² = 256

• x² + y² = 8

• x² + y² = 64

• x² + y² = 16

Multiple Choice

The diameter of a circle has length 12. The center is at (-5, 2). Give the equation of the circle.

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 144

From a Graph

• Find the coordinates of the center. Make the signs on both of them OPPOSITE before you plug them in for h and k.

• Find the radius by counting the distance from the center out to the edge of the circle. Then SQUARE that before you plug it in for r²

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Multiple Choice

What is the equation for this circle?

• (x+1)²+(y+1)²=9

• x²+y²=9

• x²+y²=6

• x²+y²=3

Multiple Choice

What is 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