Chapter 11.3, Problem 19E

To determine

To find: The equation that models the new orientation of the dish.

Answer to Problem 19E

The new equation for the satellite is $6x^2+6y^2+12xy+\sqrt{2}x-\sqrt{2}y=0$ .

Explanation of Solution

Given:

The given for the satellite tracking is $y=6x^2$ .

The angle to which the disk is rotated is $45°$ .

Calculation:

Consider the given equation is,

  $y=6x^2$

Consider the new orientation of the disk is $45°$ then, the equation is,

  $\begin{array}{l}-x^{\prime }\sin 45°+y^{\prime }\sin 45°=6{\left(x^{\prime }\cos 45°+y^{\prime }\cos 45°\right)}^2\\ -x^{\prime }\frac{1}{\sqrt{2}}+y^{\prime }\frac{1}{\sqrt{2}}=6{\left(x^{\prime }\frac{1}{\sqrt{2}}+y^{\prime }\frac{1}{\sqrt{2}}\right)}^2\\ \frac{2}{\sqrt{2}}\left(-x^{\prime }+y^{\prime }\right)=6{\left(x^{\prime }+y^{\prime }\right)}^2\\ 6x^2+6y^2+12xy+\sqrt{2}x-\sqrt{2}y=0\end{array}$