Circles, Ellipses, and Hyperbolas

Write the equation of a circle with center (7, 0) with radius 3.

• (x - 7)² + y² = 9
• x² + (y -7)² = 9
• (x - 7)² + y² = 3
• x² + (y -7)² = 3

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

See Picture

• A
• B
• C

• A
• B
• C
• D

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

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

Identify the center and the length of a and b.

• C: (0,4)  a= 25, b=4
• C: (0,0)  a= 4, b=25
• C: (0,5)  a= 2, b=5
• C: (0,0)  a= 5, b=2

Write an equation for the ellipse with each set of characteristics. Then answer the question.
Vertices ( 4, 3), (4, - 9)
Length of minor axis is 8
what is the center of this ellipse?

• (4, 6)
• ( - 4, 3)
• (6, 4)
• (4, -3)