Chapter 10.6, Problem 43AYU

To determine

To find: The derivation of the equation in $r = \frac{ep}{1 + e\text{cos}\theta }$.

Answer to Problem 43AYU

$r = ep/\left(1 + e\text{cos}\theta \right)$

Explanation of Solution

Given:

$r = \frac{ep}{1 + e\text{cos}\theta }$

Calculation:

$d\left(F, P\right) = e . d\left(D, P\right)$

$d\left(F, P\right) = p - r\text{cos}\theta$

$r = e\left(p - r\text{cos}\theta \right)$

$r = ep - er\text{cos}\theta$

$r + er\text{cos}\theta = ep$

$r = ep/\left(1 + e\text{cos}\theta \right)$