Distance and Parabolas

​Let's write an equation for a parabola.

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Equations and Graphs of Parabolas

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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.