Equations of Circles

What is the standard equation of a circle?

• (x-k)² + (y-h)² = r²

• (x+h)² + (y+k)² = r²

• (x-h)² + (y-k)² = r²

• (k-x)² + (h-y)² = r²

What does (h,k) standard for in the standard circle equation?

• (h,k) is the center of the circle

• (h,k) is a point on the circle.

• (h,k) is a point that we guess and find

• (h,k) is the distance of the circle

What does the r in the standard equation stand for?

• r is the distance of the circle

• r is the radius of the circle

• r is the x coordinate of the center of the circle

• r is the y coordinate of the center of the circle

What is the center and the radius of the circle with equation, (x-4)² + (y-2)² = 25

• Center is (5,2) and radius is 4.

• Center is (2,5) and radius is 4

• Center is (2,4) and radius is 5

• Center is (4, 2) and radius is 5

What is the center and radius of a circle with the equation, (x-1)² + (y-3)² = 4

• Center is (1,3) and radius is 2

• Center is (3,1) and radius is 2

• Center is (3,2) and radius is 1

• Center is (2,3) and radius is 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

The diameter of a circle has length 12. The center is at (-5, 2). Give 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

In order to convert from general form to center-radius form, you must ___________. 

• Multiply out
• expand
• factor
• complete the square

Determine the center and radius: x² + y² + 14x - 2y = -1

• center= (-7,2) radius= 3
• center= (-7,1) radius= 7
• center= (-4,1) radius= 5

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