Chapter 9, Problem 35CLT

To determine

Calculate the angle $\theta$ through which the axes are rotated and also draw the graph.

Answer to Problem 35CLT

The angle $\theta$ is $0.66$ .

Explanation of Solution

Given: It is given in the question that the equation is $x^2-4xy+2y^2=6$ .

Concept Used:

In this, use the Graphing utility and use the formula of rotating of axes $\cot 2\theta =\frac{A-C}{B}$ .

Calculation:

The graph is:

  

The equation is $x^2-4xy+2y^2=6$ .

Since, $A=1,B=-4,C=2$ .

The rotation angle, $\theta$ , that seek to translate from the xy − plane to the XY − plane and remove the xy − term is given by:

  $\begin{array}{l}\cot 2\theta =\frac{A-C}{B}\\ \cot 2\theta =\frac{1-2}{-4}\\ \cot 2\theta =\frac{1}{4}\\ 2\theta =1.32\\ \theta =\frac{1.32}{2}=0.66\end{array}$

Conclusion:

The $\theta$ is $0.66$ .