Chapter 12.4, Problem 1E

Interpretation Introduction

Interpretation:

To prove time delay trajectory for the following figure traces an ellipse for $0<\tau <\frac{\pi }{2}$

Concept Introduction:

• The general format of the ellipse equation is

  ${\text{Ax}}^{\text{2}}{\text{+ Bxy + Cy}}^{\text{2}}\text{+ Dx + Ey + F = 0}$

  A, B, C, D, E, F are constants and $\text{(x,y)}$ is a set of points.

• The condition for non-degenerate real ellipse is,

  ${\text{B}}^{\text{2}}-\text{4AC}<0$ and

  $C\left|\begin{array}{ccc}A& \frac{B}{2}& \frac{D}{2}\\ \frac{B}{2}& C& \frac{E}{2}\\ \frac{D}{2}& \frac{E}{2}& F\end{array}\right|=C\Delta <0$

  If $C\Delta >0$, ellipse is imaginary, and if $\Delta =0$, then ellipse is a point.