Parabola with Focus and Directrix

The vertex is sometimes halfway between the focus and directrix.

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

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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

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:
-(1/40)x² = y

• Vertex: (0, 0) Focus: (-20,0) Directrix: x = 10
• Vertex: (0, 0) Focus: (0,10) Directrix: y=10
• Vertex: (0, 0) Focus: (0,10) Directrix: y=-10
• Vertex: (0, 0) Focus: (0, -10) Directrix: y = 10

If given the equation y = 3(x + 5)² - 4, what is the vertex of the parabola?

• (5, -4)
• (-5, -4)
• (-15, -4)
• (15, -4)

The focus is always inside the parabola.

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What is the directrix of the parabolic conic section y=x²?

• y =1/4
• x=1
• y=-1/4
• y=1

Which equation below represents a parabola that opens upward with a vertex at (-5, 0)?

• y = x² + 5
• y = x² - 5
• y = (x - 5)²
• y = (x + 5)²

The 'p' value represents the distance between the vertex and the focus AND the vertex and the directrix.

• True
• False