Chapter 10 - Section 10.6 - Conic Sections in Polar Coordinates - 10.6 Exercises - Page 688: 3

$r= \dfrac{6}{2 + 3 sin(θ)}$

The polar equation of a conic with eccentricity $e$ and a horizontal line directrix is: $r= \dfrac{ed}{1 + e sin (θ)}$ Given: e = 1.5, directrix $y=2$ and Focus: $F (0,0)$ , thus $d= 2$ Now we have $r= \dfrac{ed}{1 + e sin (θ)}= \dfrac{(1.5) (2)}{1 + (1.5) \sin(θ)}$ Hence, $r= \dfrac{6}{2 + 3 \sin(θ)}$