Finding the point on an ellipse at which the normal is furthest from the centre



Consider the ellipse defined by the equation tex2html_wrap_inline15. At any point (x,y) on this ellipse there is both a tangent to the ellipse and a normal to the ellipse. (The normal at a point on a curve is defined to be the line perpendicular to the tangent.) Find the point on the ellipse whose normal line is furthest from the centre. (The distance between a point p and a line L is defined to be the length of the line segment which is perpendicular to the line L and goes from p to L.)




Instructor

Juris Steprans
email address: steprans@mathstat.yorku.ca
Department of Mathematics and Statistics.
Ross 624 South, ext. 33952
York University
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