IXL - Find the focus or directrix of a parabola (Geometry practice)

What is the focus of the parabola

Simplify any fractions.

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Learn with an example

question

What is the focus of the parabola

–

Simplify any fractions.

key idea

A parabola is the set of points in a plane that are the same distance from a fixed line and a fixed point that is not on the line. The fixed line lies outside the parabola and is called the

directrix.

The fixed point lies inside the parabola and is called the

focus.

The vertex form of a parabola that opens up or down is

(

–

)

The vertex is

(

)

the parabola opens up. If

the parabola opens down.

The distance from the vertex to the focus and the directrix is

It is called the focal length or focal distance.

The line through the focus and perpendicular to the directrix is the axis of

symmetry.

The axis of symmetry passes through the vertex and divides a parabola into two parts that are mirror images.

solution

To find the focus, first find the vertex. Then, calculate the distance from the vertex to the focus using the formula

where

is the dilation factor. Determine which direction the parabola opens and use the fact that the focus lies inside the parabola to find its coordinates.

Find the vertex.

The parabola is in vertex form. Identify the vertex.

–

(

–

)

Its vertex is

(

)

Find the distance from the vertex to the focus.

Use the dilation factor

–

to find

the distance from the vertex to the focus.

–

Determine which direction the parabola opens.

The parabola has a squared

-term,

so it could be written in the form

(

–

)

That means it opens either up or down. The dilation factor

is negative, so the parabola opens down.

Since the focus lies inside the parabola, it is

units directly below the vertex,

(

)

So, the focus is

–

Looking for more? Try these:

Lesson: Parabolas

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Z.1Find the vertex of a parabola

Lesson: Parabolas

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