Chapter 9.7, Problem 39PPS

(a)

To determine

To solve: The equation for y

Answer to Problem 39PPS

The equation for y are $900\sqrt{\left(1-\frac{x^2}{{\left(300\right)}^2}\right)}$ and $690\sqrt{\left(1-\frac{x^2}{{\left(600\right)}^2}\right)}$

Explanation of Solution

Given:

The equation is given as,

  $\begin{array}{l}\frac{x^2}{{\left(300\right)}^2}+\frac{y^2}{{\left(900\right)}^2}=1\\ \frac{x^2}{{\left(600\right)}^2}+\frac{y^2}{{\left(690\right)}^2}=1\end{array}$

Calculation:

Solve the first equation.

  $\begin{array}{l}\frac{x^2}{{\left(300\right)}^2}+\frac{y^2}{{\left(900\right)}^2}=1\\ \frac{y^2}{{\left(900\right)}^2}=1-\frac{x^2}{{\left(300\right)}^2}\\ y=900\sqrt{\left(1-\frac{x^2}{{\left(300\right)}^2}\right)}\end{array}$

Solve second equation.

  $\begin{array}{l}\frac{x^2}{{\left(600\right)}^2}+\frac{y^2}{{\left(690\right)}^2}=1\\ \frac{y^2}{{\left(690\right)}^2}=1-\frac{x^2}{{\left(600\right)}^2}\\ y=690\sqrt{\left(1-\frac{x^2}{{\left(600\right)}^2}\right)}\end{array}$

Thus, the equation for y are $900\sqrt{\left(1-\frac{x^2}{{\left(300\right)}^2}\right)}$ and $690\sqrt{\left(1-\frac{x^2}{{\left(600\right)}^2}\right)}$

(b)

To determine

To find: The intersection point of y using graphing calculator.

Answer to Problem 39PPS

The intersection point of y using graphing calculator are $\left(209,647\right),\left(-209,647\right),\left(209,-647\right),\left(-209,-647\right)$

Explanation of Solution

Given:

The equation is given as,

  $\begin{array}{l}\frac{x^2}{{\left(300\right)}^2}+\frac{y^2}{{\left(900\right)}^2}=1\\ \frac{x^2}{{\left(600\right)}^2}+\frac{y^2}{{\left(690\right)}^2}=1\end{array}$

Calculation:

Please find the attached screenshots of the calculator.

  

  

Trace the results.

  

Thus, the intersection point of y using graphing calculator are $\left(209,647\right),\left(-209,647\right),\left(209,-647\right),\left(-209,-647\right)$

(c)

To determine

To find: the comparison of the orbits.

Answer to Problem 39PPS

The orbit of satellite 2 is closer to a circle that orbit of satellite 1.

Explanation of Solution

Given:

The equation is given as,

  $\begin{array}{l}\frac{x^2}{{\left(300\right)}^2}+\frac{y^2}{{\left(900\right)}^2}=1\\ \frac{x^2}{{\left(600\right)}^2}+\frac{y^2}{{\left(690\right)}^2}=1\end{array}$

Calculation:

The orbit of satellite 2 is closer to a circle that orbit of satellite 1.

Thus, the orbit of satellite 2 is closer to a circle that orbit of satellite 1.