Equations of Circles

What is the formula for an equation of a circle?

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CCSS.HSG.GPE.A.1

Let (x, y) represent a point on a circle centered at the origin.

Determine the equation of the circle and justify your reasoning.

• The equation of the circle is (x + y)² = r² because the curvature of the circle is formed by a quadratic relationship.

• The equation of the circle is x² + y² = r² because the Pythagorean Theorem can be used to describe all points equidistant from the origin with a radius of r.

• The equation of the circle is x + y = r because the radius of the circle is always equal to the sum of the x and y coordinates.

• The equation of the circle is x² + y² = r because the distance formula can be used to determine all points equidistant from the origin with a radius of r.

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CCSS.HSG.GPE.A.1

Point B is located on circle A, as shown below.

Determine the equation of circle A.

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CCSS.HSG.GPE.A.1

Determine the equation for the graphed circle.

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CCSS.HSG.GPE.A.1

Determine the equation of the given circle.

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CCSS.HSG.GPE.A.1

Determine the equation of the circle.

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CCSS.HSG.GPE.A.1

When graphed, circle C has a diameter with endpoints on the circle at points A and B .

Which is the correct equation for circle C ?

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CCSS.HSG.GPE.A.1

What is the equation of the circle with a radius of 5 and center at (2, 3)?

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CCSS.HSG.GPE.A.1

Given a circle with the equation

(x−2)²+(y+6)²=36 ,

which of the following represents the center and radius of the circle?

• center (−2, 6); radius = 6

• center (2, -6); radius = 6

• center (−2, 6); radius = 36

• center (2, -6); radius = 36

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CCSS.HSG.GPE.A.1

A circle is represented by the equation 

(x−1)²+(y+5)²=6 . Which of the following shows the location of the center of the circle and its radius?

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CCSS.HSG.GPE.A.1