again, find the equation of the parabola with the given fetures.
focus (0,2) directrix x=2
please explain step by step if possible!
Definitnion:A parabola is a set of point that are equidistant from a given point (focus) and a given line (directrix)Originally Posted by mattballer082
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,
Kill the unneccesarry,
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: