Equations of Circles

A circle has the equation x² + y² - 12x + 8y + 3 = 0. Write the equation in standard form.

• (x - 6)² + (y + 4)² = 49

• (x + 4)² + (y - 6)² = 49

• (x - 6)² + (y + 4)² = 55

• x² + y² = 55

Tags

CCSS.HSG.GPE.A.1

What is the center for the circle with this equation x² + y² + 4x + 6y - 36 = 0?

• (-2, 5)

• (2, 7)

• (-2, -7)

• (-2, -3)

Tags

CCSS.HSG.GPE.A.1

Convert the equation of the circle from general to standard form.

• A

• B

• C

• D

Tags

CCSS.HSG.GPE.A.1

Select the matching graph.

• 
• 
• 
• 

Tags

CCSS.HSG.GPE.A.1

​ (a)   ​ is the ​radius

​ (b)   ​ is x-coordinate of the center

​ (c)   ​ ​ is the y-coordinate of the center

• r

• k

• h

• x

• y

Tags

CCSS.HSG.GPE.A.1

Write the standard equation of the circles for the following centers and radii: a. Center (0, 0), r = 2.5 ​ + ​ = ​

• 6.25

• 2.5

• 5

Tags

CCSS.HSG.GPE.A.1

Tags

CCSS.HSG.GPE.A.1

Write the equation of the circle whose diameter’s endpoints are (-4, 1) and (4, -5).

Mathematical Equivalence

ON

Tags

CCSS.HSG.GPE.A.1

Write the equation of a circle with center (7, 0) with radius 5.

Mathematical Equivalence

ON

Tags

CCSS.HSG.GPE.A.1

The equation of a circle is x² + y² + 6x - 12y + 20 = 0. Write the equation in standard form.

• (x - 3)² + (y + 6)² = 25

• (x + 3)² + (y - 6)² = 25

• (x - 3)² + (y + 6)² = 45

• (x + 3)² + (y - 6)² = 5

Tags

CCSS.HSG.GPE.A.1