Deriving and Using the Equation of a Circle

• Center: (0,0) Radius: 9

• Center: (-2, 4) Radius: 9

• Center: (1,1) Radius: 18

• Center: (-2, 2) Radius: 18

Tags

CCSS.HSG.GPE.A.1

The endpoints of a diameter of a circle are (−3,1) and (9,6).Find the equation of the circle? Hint: In this problem, we are not given the center or radius however we can find the length of the diameter using the distance formula (Phythagoras) and then divide it by 2. The center is simply the midpoint of the given points.

• (x−5)²+(y−7/2)²=169/4

• (x−3)²+(y−3)²=169/4

• (x−3)²+(y−7/2)²=169/4

• (x−7/2)²+(y−7/2)²=169/4

Tags

CCSS.HSG.GPE.A.1

Write the equation of the graphed circle.

• x² + (y + 3)² = 3

• x² + (y – 3)² = 3

• x² + (y + 3)² = 9

• x² + (y – 3)² = 9

Tags

CCSS.HSG.GPE.A.1

Determine the center of the circle given the equation (x+2)^2 + (y-1)^2 = 36

• (3, 4)

• (5, -2)

• (0, 0)

• (-2, 1)

Tags

CCSS.HSG.GPE.A.1

The equation given represents the equation of a circle. What is the radius of the circle?

x² + y² - 4x + 12y +15 = 0

• 6

• 5

• 4

• 7

Tags

CCSS.HSG.GPE.A.1

See Picture

• A

• B

• C

Tags

CCSS.HSG.GPE.A.1

Tags

CCSS.HSG.GPE.A.1

Determine the equation of the circle in standard form: x² + y² + 6x - 12y + 20 = 0

• (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

• (-1,4)

• (1,4)

• (-1,-4)

• (1,-4)

Tags

CCSS.HSG.GPE.A.1

The equation (x+3)²+(y-5)²=r² represents circle A. The point B(0,6) lies on the circle. What is r, the length of the radius of circle A?

• √13

• 2

• 10

• √10

Tags

CCSS.HSG.GPE.A.1