Parabola secant line and perpendicular bisector.

Author:: Mitch Keller

Topic:: Calculus, Geometry, Parabola

Click on the point

and drag it to see what happens with

as

approaches the origin

. Use an appropriate limit to find the limiting position of

or to explain why there is no limiting position.

Suppose that the -coordinate of point is . What is the -coordinate of ?
Find the coordinates of the midpoint of line segment .
Let be the -coordinate of the point . Find a formula for in terms of .
Use an appropriate limit to determine what happens with as approaches the origin. If your result seems counterintuitive, use the GeoGebra applet above to validate what you've found.