Solution Found!
Sketch the following conic sections, giving axes of symmetry and asymptotes (if any). a
Chapter 6, Problem 16(choose chapter or problem)
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,