Find the points on the ellipsoid x^2 + 2y^2 + 3z^2 = 1 where the tangent plane is parallel to the plane 3x - y + 3z = 1 I have no idea how to do this, but i do have a knowledge of partial derivatives, its my first yr at university im 17.
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Originally Posted by Brennox Find the points on the ellipsoid where the tangent plane is parallel to the plane I have no idea how to do this, but i do have a knowledge of partial derivatives, its my first yr at university im 17. You need to find the point(s) on the ellipsoid at which its gradient is parallel to the normal of the plane.
Originally Posted by Plato You need to find the point(s) on the ellipsoid at which its gradient is parallel to the normal of the plane. yea and how do i do that??
Originally Posted by Brennox yea and how do i do that?? You first find the gradient to the surface. What is it?
Originally Posted by Plato You first find the gradient to the surface. What is it? Ok im not rly sure what im doing but, do i find partial derivatives? 2x, 4y, 6z then for 2nd eq its 3, -1, 3 If im not on the right track can you please show me the method
Originally Posted by Brennox Ok im not rly sure what im doing but, do i find partial derivatives 2x, 4y, 6z then for 2nd eq its 3, -1, 3 Now you want . Solve for and substitute into the surface. Solve for .
Originally Posted by Plato Now you want . Solve for and substitute into the surface. Solve for . So x = 3/2t, y = -1/4t and z = 1/2t (3/2t)^2 + 2(-1/4t)^2 + 3(1/2t)^2 = 1 [eq 1] 9/2t + 1/4t + 3/2t = 1 [eq 2] So is this right? if so.. after solving for t and finding the values of x,y and z is that my final answer? How do i know these are parallel?
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