## Calculus 8th Edition

a) Let us consider the points $A$ on the conic section, whose focus is $f$ and directrcix is $L$. Thus, the eccentricity$(e)$ can be calculated as: $e=\dfrac{|Af|}{|AL|}$; where, $\dfrac{|Af|}{|AL|}$ is a fixed ratio. b) For an ellipse: $e \lt 1$ For a hyperbola: $e \gt 1$ For a parabola: $e = 1$ c) For a conic section with eccentricity $(e)$ and directrx $x=d$, the polar equation can be represented as: $r=\dfrac{ed}{(1+e \cos \theta)}$; for directrix: $x=d$; $r=\dfrac{ed}{(1-e \cos \theta)}$; for directrix: $x=-d$; $r=\dfrac{ed}{(1+e \sin \theta)}$; for directrix: $y=d$; $r=\dfrac{ed}{(1-e \sin \theta)}$; for directrix: $y=-d$;