SOLUTION: The equation of an ellipse with center (4,3) that passes through the points (8,3) and (4,5) has the form f(x,y)=1. Find f(x,0).

We plot those three points:



And now we can sketch the ellipse:



and draw 'a' and 'b'.

We can tell that a=4 and b=2 by counting units:



The equation is

  

  

  

Since   f(x,y) ,

The above graph is a cross section of a 3D eliptic paraboloid, when
sliced at the plane where z=1.  We are to find f(x,0) 

        f(x,y)

and     f(x,0)

        f(x,0)

        f(x,0)

        f(x,0)

That is a parabola which is a cross section of the same 3D elliptic
paraboloid when sliced by the xz-plane.

Edwin