Circles and conic sections

The diameter of a circle has length 12. The center is at (-5, 2). What is the equation of the circle?

• (x - 2)² + (y + 5)² = 36

• (x - 5)² + (y + 2)² = 6

• (x + 5)² + (y - 2)² = 36

• (x + 2)² + (y - 5)² = 6

Tags

CCSS.HSG.GPE.A.1

What is the center of (x + 2)²  + (y - 5)² = 25

• (-2,5)
• (2,-5)
• (2,5)
• (-1,-5)

Tags

CCSS.HSG.GPE.A.1

Jemilie and Nathaley are helping their friend Archie to design a circular garden in his backyard. Archie wants the garden to be in the shape of the circle represented by the standard form equation (x+3)^2 + (y-4)^2 = 36. Can you help Jemilie, Nathaley and Archie figure out the location and size of the garden?

• The garden will be centered at (-3, 4) with a radius of 12 feet.

• The garden will be centered at (3, -4) with a radius of 36 feet.

• The garden represented by the standard form equation (x+3)^2 + (y-4)^2 = 36 will be centered at (-3, 4) with a radius of 6 feet.

• The garden will be centered at (0, 0) with a radius of 9 feet.

Answer explanation

The circle with the equation (x+3)^2 + (y-4)^2 = 36 is centered at (-3, 4) with a radius of 6.

Tags

CCSS.HSG.GPE.A.1

What is the equation of the circle, with centre (-2,-7) and radius 3 units?

• (x + 2)^2 + (y + 7)^2 = 3
• (x - 2)^2 + (y - 7)^2 = 9
• (x + 2)^2 + (y + 7)^2 = 9
• (x - 2)^2 + (y - 7)^2 = 3

Tags

CCSS.HSG.GPE.A.1

Which equation matches the circle on the graph?

• (x-3)² + (y-4)² = 16

• (x-5)² + (y-2)² = 20

• (x+3)² + (y+4)² = 16

• (x-9)² + (y-16)² = 32

Tags

CCSS.HSG.GPE.A.1

A circle in a coordinate plane is shown.

What is the radius of the circle?

Tags

CCSS.HSG.GPE.A.1

Circle O is defined by the equation x² + (y – 2)² = 25.  What is the center of circle O.

• (-2, 0)
• (0, 2)
• (0, -2)
• (2, 5)

Tags

CCSS.HSG.GPE.A.1

Write the equation of a circle with its diameter whose endpoints are (2,7) and (4,-3). Hint: first find the center of the circle using midpoint formula.

• (x-3)²+(y-2)²=26

• (x+3)²+(y+2)²=26

• (x+1)²+(y-5)²=13

• (x+1)²+(y-5)²=89

Tags

CCSS.HSG.GPE.A.1

What is the equation of the circle, with center (-4,5) and radius 6 units?

• (x - 4)^2 + (y + 5)^2 = 6

• (x - 4)^2 + (y + 5)^2 = 36

• (x + 4)^2 + (y - 5)^2 = 6

• (x + 4)^2 + (y - 5)^2 = 36

Tags

CCSS.HSG.GPE.A.1

What is the center of this circle?

• (2, 2)

• (2, -2)

• (0, 0)

• (-2, 2)

Tags

CCSS.HSG.GPE.A.1