Equations of a Circle Given Points

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

• (3,2)

• (-3, -2)

• (-2, -3)

• (2, 3)

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 equation of the circle, with center (4,2) and radius 5 units?

• (x + 4)² + (y + 2)² = 25

• (x + 4)² + (y + 2)² = 5

• (x - 4)² + (y - 2)² = 5

• (x - 4)² + (y - 2)² = 25

Tags

CCSS.HSG.GPE.A.1

What is the center and

the radius of this circle?

• Center: (12, 8)

  Radius = 5 units

• Center: (-12 ,8)

  Radius = 25 units

• Center: (-12,-8)

  Radius = 5 units

• Center: (12, 8)

  Radius = 25 units

Tags

CCSS.HSG.GPE.A.1

In the equation for a circle, (x-h)²+(y-k)²= r², what part of the circle do the h, k and r represent?

• r is the hypotenuse, h and k are points on the circle

• r is the radius, h and k are points on the circle

• r is the roundness, h and k represent the center

• r is the radius, h and k represent the center

Tags

CCSS.HSG.GPE.A.1

What is the center of this circle?

• (2, 4)

• (-2, 4)

• (2, - 4)

• (-2, - 4)

Tags

CCSS.HSG.GPE.A.1

Point B is located on circle A, as shown below. Determine the equation of circle A.

Tags

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.

Tags

CCSS.HSG.GPE.A.1

Determine the equation for the graphed circle.

Tags

CCSS.HSG.GPE.A.1

Determine the equation of the given circle.

Tags

CCSS.HSG.GPE.A.1