Focus and Directrix of Parabolic Equations

A parabola that opens up has a focus point at (2, 5) and a directrix at y = -1.  Write the equation of this parabola. 

Tags

CCSS.HSG.GPE.A.2

Architectural Designers is creating a schematic for a bridge over the Columbia River whose arch is in the shape of a parabola.  The road, 40 feet above the river surface, represents the directrix of the parabolic arch.  The focus of the parabolic arch is located 20 feet above the river surface.  In the schematic, the river surface will be positioned along the x-axis and the axis of symmetry for the downward opening parabolic arch will be positioned along the y-axis.  Which equation best models the parabolic arch in the schematic?

A certain parabola opens to the left, has an axis of symmetry along the x-axis, a vertex at the origin, and a distance between the focus and directrix of 5 units.  Which of the following equations models this parabola?

Find the focus, and directrix of the parabola: y² = - 32x

• Focus: (0,-8) Directrix: x= -8

• Focus: (0,-8) Directrix: y= 8

• Focus: (-8,0) Directrix: x = -8

• Focus: (-8,0) Directrix: x= 8

Find the focus and the directrix. \(x=y^2\)

• 
• 
• 
• 

Find the focus and the directrix.

• 
• 
• 
• 

Find the equation of the parabola with Focus at (7, 0) and directrix x = - 7.

Tags

CCSS.HSG.GPE.A.2

Identify the focus and directrix of the parabola: (y-2)² = 24(x-5)

• focus: (5, 7); directrix: y = -4

• focus: (5, -4); directrix: y = 7

• focus: (11, 2); directrix: y = -1

• focus: (-1, 2); directrix: y = 11

• 
• 
• 
• 

Find the equation of the parabola described:
Focus at (10, 0);   directrix the line x = -10 

•  y² = 40x

•  y² = - 40x 

•  y² = 10x 

•  x² = 40y

Tags

CCSS.HSG.GPE.A.2