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
Thanks
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 "?