Circles and Parabolas

Change the following equation to standard form
x²+y²-4x+12y-8=0

• (x+2)²+(y-6)²=48

• (x-2)²+(y+6)²=48

• (x-6)²+(y-2)²=48

• (x+2)²+(y-6)²=48

Tags

CCSS.HSG.GPE.A.1

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

Tags

CCSS.HSG.GPE.A.1

Which of the following is the length of the diameter of the circle whose equation is shown below? 
2x²+2y²-20x+24y=166

• 12

• 24

• 6

• 10

Tags

CCSS.HSG.GPE.A.1

A parabola is the set of all points equidistant from the focus and the directrix.

• true

• false

Tags

CCSS.HSG.GPE.A.2

If the directrix is y = 4 and the focus is at 
(3, 0), the value of p is:

• 8

• -8

• 2

• -2

If the directrix is y = 4 and the focus is at 
(3, 0), the equation of the parabola is:

• y = (-1/8)(x - 3)² + 2

• x = (-1/8)(y - 2)² + 3

• y = (1/8)(x - 3)² + 2

• x = (1/8)(y - 2)² + 3

Find the standard form of the equation of the parabola whose focus (0, 4) and a directrix y=-4.

• y = (1/16)x²

• y² = 4x

• y² = 16x

• y = (1/4)x²

Tags

CCSS.HSG.GPE.A.2

Find the vertex, focus, and directrix of the parabola: x² = 28y

• Vertex: (0, 0) Focus: (0,7) Directrix: y=-7

• Vertex: (0, 0) Focus: (7,0) Directrix: y=7

• Vertex: (0, 0) Focus: (0,-7) Directrix: x=-7

• Vertex: (0, 0) Focus: (7, 0) Directrix: x=7

(y-4)² = -8(x+1)
What are the coordinates for the focus?

• (1,4)

• (-1,6)

• (-1,2)

• (-3,4)

The vertex, (h, k), is halfway between the focus and the directrix.

• true

• false