A parabola has the parametric equations x = 2at and y = at^2. The normal to the parabola when t= p is Show that through it is possible to draw up to three normals to the parabola

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- Jan 15th 2010, 07:51 PMdifferentiateshowing that 3 normals can be drawn to parabola
A parabola has the parametric equations x = 2at and y = at^2. The normal to the parabola when t= p is Show that through it is possible to draw up to three normals to the parabola

(Wink)

Thanks - Jan 15th 2010, 08:56 PMIsomorphismGeometry+Algebra = Analytical Geometry
Geometry: The point lies on the line for some .

Algebra: Substitute in

Geometry: To prove that it is possible to draw up to three normals to the parabola of the form .

Algebra: To prove that it is possible that there are up to three solutions for the equation .

Now that we have formulated the problem algebraically, can you tell why "there are up to three solutions for the equation "?