Equations of Circles in the Coordinate Plane

Determine the equation of the circle in standard form:
x² + y² + 4x + 6y - 36 = 0

• (x+2)² + (y+3)² = 49

• (x+2)² + (y+3)² = 13

• (x-2)² + (y-3)² = 49

• (x-2)² + (y-3)² = 13

Tags

CCSS.HSG.GPE.A.1

Match each equation to its description.

• Circle centered at (1, -4) and radius √3

• x² + (y + 4)² = 9

• Circle centered at (1, -4) and radius 3

• (x – 1)² + (y – 4)² = 3

• Circle centered at (1, 0) and radius 3

• (x – 1)² + (y + 4)² = 9

• Circle centered at (0, -4) and radius 3

• (x – 1)² + (y + 4)² = 3

• Circle centered at (1, 4) and radius √3

• (x – 1)² + y² = 9

Tags

CCSS.HSG.GPE.A.1

Plot the circles x² + y² = 4 and x² + y² = 1 on the same coordinate plane.

Which equation of a circle is centered at (-3, 2) and has a radius of 5?

• (x + 3)² + (y - 2)² = 25

• (x - 3)² + (y + 2)² = 5

• (x + 3)² + (y - 2)² = 5

• (x - 3)² + (y + 2)² = 25

Tags

CCSS.HSG.GPE.A.1

In the equation (x-4)²+(y-3)²=25, the radius is

• 4

• 3

• 5

• 25

Tags

CCSS.HSG.GPE.A.1

Mathematical Equivalence

ON

Tags

CCSS.HSG.GPE.A.1

Determine the equation of the circle with :

center (−6 , −2 ) containing the point ( 3, −6 ).

Mathematical Equivalence

ON

Tags

CCSS.HSG.GPE.A.1

Determine the center and radius:
x² + y² - 10x + 8y -8 = 0

• C = (5,-4) r = 7

• C = (-5,4) r = 7

• C = (-4,5) r = 49

• C = (5,-4) r = 49

Tags

CCSS.HSG.GPE.A.1

What are the coordinates of the center and the radius of the circle with equation:
(x - 4)² + (y - 3)² = 25 ?

• Center (4,3)
  Radius = 5 units

• Center (4,3)
  Radius = 25 units

• Center (-4,-3)
  Radius = 25 units

• Center (-4,-3)
  Radius = 5 units

Tags

CCSS.HSG.GPE.A.1

What is the center of the circle with equation x² + y² = 1?

• (1, 1)

• (0, 0)

• not enough information

Tags

CCSS.HSG.GPE.A.1