Question

Write the equation of the conic section satisfying the given conditions. focus at the pole, e = 3/4, horizontal directrix 2 units above the pole

Answer 1

Answer:

The equation in the polar form is;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$

Step-by-step explanation:

 e = 3/4  > 1, we have an hyperbola    

The polar equation of a conic is of the form;

For vertical directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot cos (\theta)}$

For horizontal directrix

$r = \dfrac{k \cdot e}{1\pm e \cdot sin(\theta)}$

Where;

k = Distance from the focus to the directrix = 2

We have;

$r = \dfrac{2 \cdot \dfrac{3}{4} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

$r = \dfrac{\dfrac{3}{2} }{1 + \dfrac{3}{4} \cdot sin(\theta)}$

Which gives the equation in the polar form as follows;

$r = \dfrac{6}{4 + 3 \cdot sin(\theta)}$.