again, find the equation of the parabola with the given fetures.

focus (0,2) directrix x=2

please explain step by step if possible!

thank you

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- July 23rd 2006, 04:05 PMmattballer082this one is confusing me
again, find the equation of the parabola with the given fetures.

focus (0,2) directrix x=2

please explain step by step if possible!

thank you - July 23rd 2006, 05:18 PMThePerfectHackerQuote:

Originally Posted by**mattballer082**

**Definitnion:***A parabola is a set of point that are equidistant from a given point (focus) and a given line (directrix)*

Let be a point on the parabola. Then it is equidistant from the focus and the line, . The distance to the focus by the distance formula is,

Now, what is distance to the line . This is slightly difficult. To find the distance from a point to a line you need to draw a perpendicular line, then find the distance of that line. Note, the is a vertical line, that means if you draw (and try to imagine this) a perpendicular line from the point you intersect at . Now the distance between these two points is,

By, definition these two distances are equal hence,

Square both sides,

Thus,

Kill the unneccesarry,

Rewrite as,

- July 24th 2006, 06:32 AMSoroban
Hello, mattballer0821

Quote:

Find the equation of the parabola with the given features.

Focus (0,2) directrix x=2

You're expected to know these basic facts . . .

The Vertex is halfway between the Focus and the Directrix.

There are two forms:

. . . . Vertical: . . . opens up or down: or

. . Horizontal: . . . opens right or left: or

where is the Vertex of the parabola

and is the*directed*distance from the Vertex to the Focus.

The parabola always "bends around" the Focus.

The parabola always "bends away" from the Directrix.

Sketch the given information:Code:`o |`

|o :

| o :

F(0,2)* oV :

| o :

- - - - +o- - - + -

o | :

| -x=2

We see that the Vertex is

. . the parabola opens to the left:

. . distance from Vertex to Focus is to the__left__:

Therefore: .