Polar Equations of Conics

Concept:

The equations of conic sections in polar form take an especially simple and unified form when a focus is at the pole and an axis is parallel or perpendicular to the ray θ = 0°.

r =	pe
	(1 - e cos θ)

r =	pe
	(1 + e cos θ)

r =	pe
	(1 - e sin θ)

r =	pe
	(1 + e sin θ)

Changing the sign in the denominator or changing the trigonometric function used in the denominator to the sine function changes the orientation of the graph, but not its shape or size.

ellipse	parabola	Hyperbola

$0 < e <1$	$e = 1$	$e > 1$
Click on the picture of the conic section you want to investigate.

sign in denominator:	+ -	equation: r =
trig function:	sine cosine	equation: r =

sign in denominator:	+ -	equation: r =
trig function:	sine cosine	equation: r =

sign in denominator:	+ -	equation: r =
trig function:	sine cosine	equation: r =

vertices: (, ) and (,)	foci: (0,0) and (,)	transverse axis:
covertices: (,) and (,)	center: (,)	conjuate axis:
directrices: = and =	asymptotes: = x and = x

Polar Equations of Conics

Concept:

INSTRUCTIONS

EXPLORATIONS

PRACTICE QUESTIONS