Calculus
# Polar Equations

The Earth and Mars' orbits are approximated by elliptical functions. When placed on the same coordinate system with the Sun at the center, the two orbits are approximated by the polar equations

$A: r= \frac{1 - (.03)^2}{1+.03\cos\theta}$

and

$B: r= 1.52\left(\frac{1 - (.09)^2}{1+.09\cos\theta}\right).$

Which is the equation for Earth's orbit?

The equation

$(x^2 + y^2)^3 = (x^2 - y^2)^2,$

whose graph is shown, describes a *Quadrifolium*. What is its equation in polar coordinates?

$0 \leq \theta \leq 2\pi,$ the graph of an *Archimedian Spiral* with equation $r = \theta,$ and an *involute of a circle* having equation $r = \sqrt{1 + \theta^2}.$

Which is the graph of the Archimedean Spiral?

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