I have the following problem:
The point P lies on the ellipse and N is the foot of the perpendicular from P to the line x = 2 (see attachment). Find the equation of the mid point of PN as P moves on the ellipse.
My answer does not agree with the one in my maths book, so I would just like to confirm whether the book is correct or not. Secondly, I have solved this problem using the parametric form of the point and as far as I can see, it is the only way to solve this problem - but I thought the parametric form was simply an alternate formulation of the ellipse and therefore there should be a way of solving the question without using the parametric form. Is this right?
So comparing with we have a = 1 and b =
and N(2,y) so the mid point is
My maths book gives: