Solution Found!
Quadric surfaces Consider the following
Chapter 12, Problem 57E(choose chapter or problem)
Quadric surfaces Consider the following equations of quadric surfaces.
(a) Find the intercepts with the three coordinate axes, when they exist.
(b) Find the equations of the xy-, xz-, and yz-traces, when they exist.
(c) Sketch a graph of the surface.
Hyperboloids of two sheets
\(-x^{2}+\frac{y^{2}}{4}-\frac{z^{2}}{9}=1\)
Questions & Answers
QUESTION:
Quadric surfaces Consider the following equations of quadric surfaces.
(a) Find the intercepts with the three coordinate axes, when they exist.
(b) Find the equations of the xy-, xz-, and yz-traces, when they exist.
(c) Sketch a graph of the surface.
Hyperboloids of two sheets
\(-x^{2}+\frac{y^{2}}{4}-\frac{z^{2}}{9}=1\)
ANSWER:Solution 57EStep 1 of 3:Given : Surface is = 1a) In this problem we need to find the intercepts with the three coordinate axes . X-intercept: The point ( x , y , z) at which the hyperboloid intersects the x-axis must have y = z =0 .Substitute y = z = 0 in the above equation we get : = 1 Therefore , the given surface has no x -intercept. Y-intercept: The point ( x , y , z) at which the hyperboloid intersects the y-axis must have x = z =0 .Substitute x = z = 0 in the above equation we get : = 1 Therefore , the given surface has y-intercept at -2 , 2 Z-intercept: The point ( x , y , z) at which the hyperboloid intersects the z-axis must have y = x =0 .Substitute y = x= 0 in the above equation we get : = 1 Therefore , the given surface has no z-intercept.