# Parametric equations for Tangent line of an ellipse

by derek1999
Tags: ellipse, equations, line, parametric, tangent
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,569 You are being much too complicated! First the problem asked for parametric equations for the tangent line. It is not necessary to get parametric equations for the ellipse,. Yes, with y= 2, your equation reduces to $4x^2+ z^2= 8$. From that you can calculate immediately that $8x + 2z dz/dx= 0$ so that $dz/dx= -4x/z$. In particular, at x= 1, z= 2, $dz/dx= -4(1)/2= -2$. The tangent line through that point, in the y= 2 plane, is z= -2x+ 4. Now, to get parametric equations of the line in three dimensions, take x= t as parameter: x= t, y= 2, z= -2t+ 4.