Parabola with Focus and Directrix

How do we define a parabola using its focus and directrix?

• A parabola is the set of all points that are the same distance from a single point, called the focus of the parabola, and a line, called the directrix of a parabola.

• A parabola is the set of all points that have a greater y value than a single point, called the focus of the parabola, and a lesser x value than a single point, called the directrix of the parabola.

• A parabola is a circle with a center point called the focus of the parabola, and a line from the center of the circle to the circle called the directrix of the parabola.

• A parabola is a square in which the center of the square is called the focus of the parabola, and the length of one side of the square is called the directrix of the parabola.

Each point on the curve of a parabola is ____________ to focus and the directrix.

• equilateral

• perpendicular

• equidistant

• tangent

Tags

CCSS.HSG.GPE.A.2

What is the standard equation of a parabola with Focus (1,3) and the directrix is 6 units to the left of the focus?

Tags

CCSS.HSG.GPE.A.2

What is the standard equation of a parabola with Focus (2,5) and the directrix is 6 units to the right of the focus?

Tags

CCSS.HSG.GPE.A.2

What is the focus of the parabola (y-5)^2=12(x-2)?

What is the vertex and focus of the parabola (y-2)^2=-16(x-3)?

• Vertex: (-3, -2) Focus: (-3, 14)

• Vertex: (-3, -2) Focus: (-3, -18)

• Vertex: (3, 2) Focus: (-1, -2)

• Vertex: (3, 2) Focus: (-1, 2)

What is the standard form of the equation of the parabola with Focus: (0, 7) and the vertex at the origin?

Tags

CCSS.HSG.GPE.A.2

What is the standard equation of a parabola with Vertex (4,3) and the focus is 2 units above the vertex?

What is the standard equation of a parabola with Vertex (-2, 1) and the directrix is 4 units below the vertex?

Given the graph below, what is the equation of the parabola?