Parameterize the curve of intersection of the cylinder x^2 y^2 = 16 and the plane x z = 5 Homework Equations The Attempt at a Solution i think i must first parameterize the plane x = 5t, y = 0, z = 5t then i think i plug those into the eq of the cylinder 25t^2 = 16 t = 8 so x = 4, y = o, z = 4, am i on the right track, i feel like iY are given by the "shadow" of the cone To locate that shadow set z = x/x2 y2 equal to z = a The plane cuts the cone at the circle x2 y2 = a2 We integrate over the inside of that circle (where the shadow is) surface area of cone = f 2 dx dy = /2 na 2 shadow EXAMPLE 4 Find the same area using dS = /2 u du dv from Example 2The equation $x^2y^2y=0$ can be rewritten $x^2(y\frac 12)^2=\cfrac 14$ For any value of $z$ this is a circle, so you should be able to see how this makes the figure a cylinder (like a straight line, a cylinder in this terminology has no ends) Share Cite Follow
Solution Solution The Given Solid Is The Region Outside The Cylinder X 2 Y 2 9 Course Hero
