Quadric surfaces Consider the following

Chapter 12, Problem 57E

(choose chapter or problem)

Get Unlimited 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

\(-x^{2}+\frac{y^{2}}{4}-\frac{z^{2}}{9}=1\)

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.

Add to cart


Study Tools You Might Need

Not The Solution You Need? Search for Your Answer Here:

×

Login

Login or Sign up for access to all of our study tools and educational content!

Forgot password?
Register Now

×

Register

Sign up for access to all content on our site!

Or login if you already have an account

×

Reset password

If you have an active account we’ll send you an e-mail for password recovery

Or login if you have your password back