Sketch the following conic sections, giving axes of symmetry and asymptotes (if any). a

Chapter 6, Problem 16

(choose chapter or problem)

Get Unlimited Answers
QUESTION:

Sketch the following conic sections, giving axes of symmetry and asymptotes (if any). a. 6x1x2 8x2 2 = 9 b. 3x2 1 2x1x2 + 3x2 2 = 4 c. 16x2 1 + 24x1x2 + 9x2 2 3x1 + 4x2 = 5 d. 10x2 1 + 6x1x2 + 2x2 2 = 11 e. 7x2 1 + 12x1x2 2x2 2 2x1 + 4x2 = 6

Questions & Answers

QUESTION:

Sketch the following conic sections, giving axes of symmetry and asymptotes (if any). a. 6x1x2 8x2 2 = 9 b. 3x2 1 2x1x2 + 3x2 2 = 4 c. 16x2 1 + 24x1x2 + 9x2 2 3x1 + 4x2 = 5 d. 10x2 1 + 6x1x2 + 2x2 2 = 11 e. 7x2 1 + 12x1x2 2x2 2 2x1 + 4x2 = 6

ANSWER:

Step 1 of 5

The conic section,  can be written in the matrix form as,

The characteristic equation of  is determined as,

 Then, the diagonalisation of the matrix is determined as,

Then, the conic can be represented in  and  as,

.

This is of the form of a Hyperbola.

Therefore, the asymptote is determined as,

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