Distance and Parabolas

​Let's write an equation for a parabola.

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Equations and Graphs of Parabolas

Fill in the Blank

What is the directrix of this parabola?

Fill in the Blank

What is the focus of this parabola?

Equations and Distance

Parabola

A parabola is the set of points that are equidistant from a given point and a given line.

This point is the focus. The line is the directrix.

Multiple Choice

Which equation matches this graph?

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ y^2$$

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ +\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ -\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 1\right)^2\ =\ y^2$$

Multiple Choice

Which equation matches this graph?

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ y^2$$

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ +\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ -\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 1\right)^2\ =\ y^2$$

Multiple Choice

Which equation matches this graph?

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ y^2$$

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ +\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ -\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 1\right)^2\ =\ y^2$$

Multiple Choice

Which equation matches this graph?

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ y^2$$

• $$\left(x\ -\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ +\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 2\right)^2\ =\ \left(y\ -\ 1\right)^2$$

• $$\left(x\ +\ 3\right)^2\ +\ \left(y\ -\ 1\right)^2\ =\ y^2$$

Open Ended

Write an equation for this parabola.