Chapter MPS, Problem 10.5MPS

(a)

To determine

To Find: The Equation of Elliptical orbit.

Answer to Problem 10.5MPS

  $\frac{x^2}{864900}+\frac{y^2}{703921}=1$

Explanation of Solution

Given:

  $\begin{array}{l}a=930\text{ million miles}\\ b=839\text{ million miles}\end{array}$

Formula Used:

  $\begin{array}{l}\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ \frac{x^2}{b^2}+\frac{y^2}{a^2}=1\\ c^2=a^2-b^2\end{array}$

Calculation:

  $\begin{array}{l}a=930\text{ million miles}\\ b=839\text{ million miles}\\ \left(h,k\right)=\left(0,0\right)\\ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ \text{⇒}\frac{x^2}{864900}+\frac{y^2}{703921}=1\end{array}$

Conclusion:

Thus, the required equation is $\frac{x^2}{864900}+\frac{y^2}{703921}=1$ .

(b)

To determine

To Draw: The graph of parabola.

Explanation of Solution

Given:

  $\begin{array}{l}a=930\text{ million miles}\\ b=839\text{ million miles}\end{array}$

Formula Used:

  $\begin{array}{l}\frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ \frac{x^2}{b^2}+\frac{y^2}{a^2}=1\\ c^2=a^2-b^2\end{array}$

Calculation:

  $\begin{array}{l}a=930\text{ million miles}\\ b=839\text{ million miles}\\ \left(h,k\right)=\left(0,0\right)\\ \frac{x^2}{a^2}+\frac{y^2}{b^2}=1\\ \text{⇒}\frac{x^2}{864900}+\frac{y^2}{703921}=1\end{array}$

  

Conclusion:

Thus, the graph has been drawn.