8. Conic Sections

Parabolas

8. Conic Sections

# Parabolas - Video Tutorials & Practice Problems

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concept

## Parabolas as Conic Sections

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2

Problem

ProblemGraph the parabola $-4\left(y+1\right)=\left(x+1\right)^2$, and find the focus point and directrix line.

A

B

C

D

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Problem

ProblemIf a parabola has the focus at $\left(0,-1\right)$ and a directrix line $y=1$, find the standard equation for the parabola.

A

$4y=x^2$

B

$4\left(y-1\right)=x^2$

C

$-4y=x^2$

D

$-4\left(y+1\right)=x^2$

4

example

## Parabolas as Conic Sections Example 1

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5

concept

## Horizontal Parabolas

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6

Problem

ProblemGraph the parabola $8\left(x+1\right)=\left(y-2\right)^2$ , and find the focus point and directrix line.

A

B

C

D

7

Problem

ProblemIf a parabola has the focus at $\left(2,4\right)$ and a directrix line $x=-4$ , find the standard equation for the parabola.

A

$12\left(x+1\right)=\left(y-4\right)^2$

B

$-\left(x+1\right)=\left(y-4\right)^2$

C

$12x=y^2$

D

$4\left(x-1\right)=\left(y+4\right)^2$

8

example

## Horizontal Parabolas Example 1

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PRACTICE PROBLEMS AND ACTIVITIES (58)

- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. x^2 - ...
- Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (12,0); Directr...
- Identify the conic represented by the equation without completing the square. 4x^2 - 9y^2 - 8x + 12y - 144 = 0
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^...
- Identify the conic represented by the equation without completing the square. y^2 + 4x + 2y - 15 = 0
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (y-2)^...
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^...
- Identify the conic represented by the equation without completing the square. y^2 + 4x + 2y - 15 = 0
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (y-2)^...
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (x-4)^...
- Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Direct...
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. y^2 = ...
- Find the vertex, focus, and directrix of the parabola with the given equation. Then graph the parabola. (y-2)^...
- Find the standard form of the equation of the parabola satisfying the given conditions. Focus: (0,-11); Direct...
- In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equat...
- In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equat...
- In Exercises 1–4, find the focus and directrix of each parabola with the given equation. Then match each equat...
- In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabo...
- In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabo...
- In Exercises 5–16, find the focus and directrix of the parabola with the given equation. Then graph the parabo...
- In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. ...
- In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. ...
- In Exercises 17–30, find the standard form of the equation of each parabola satisfying the given conditions. ...
- In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match...
- In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match...
- In Exercises 31–34, find the vertex, focus, and directrix of each parabola with the given equation. Then match...
- In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph...
- In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph...
- In Exercises 35–42, find the vertex, focus, and directrix of each parabola with the given equation. Then graph...
- In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the v...
- In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the v...
- In Exercises 43–48, convert each equation to standard form by completing the square on x or y. Then find the v...
- In Exercises 49–56, identify each equation without completing the square. y^2 - 4x + 2y + 21 = 0
- In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's d...
- In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's d...
- In Exercises 57–62, use the vertex and the direction in which the parabola opens to determine the relation's d...
- In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the sa...
- In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the sa...
- In Exercises 63–68, find the solution set for each system by graphing both of the system's equations in the sa...