Deriving the Equation of a Circle

Identify the description that matches this equation. x^2+y^2=49

• a circle with center (0, 0) and radius 7

• a circle with center (1, 1) and radius 7

• a circle with center (0, 0) and radius 49

• a circle with center (0, 0) and radius 1

Tags

CCSS.HSG.GPE.A.1

Find the center and radius of the circle: 3x² + 3y² + 42x - 6y = -3

• center= (-7, 2) radius= 3

• center= (-7, 1) radius= 7

• center= (-4, 1) radius= 5

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 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

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

Write the equation of the circle in standard form:

• A

• B

• C

• D

Tags

CCSS.HSG.GPE.A.1

In the equation
(x+2)²+(y+3)²=49, what is the center of the circle?

• (2, 3)

• (3, 2)

• (-3, -2)

• (-2, -3)

Tags

CCSS.HSG.GPE.A.1

Which is the correct equation of the given circle?

• (x + 2)² + (y + 1)² = 2

• (x + 2)² + (y + 1)² = 4

• (x - 2)² + (y - 1)² = 2

• (x - 2)² + (y - 1)² = 4

Tags

CCSS.HSG.GPE.A.1