Integration:

Back and Forth:

Find a polar equation for the curve $$x^4 + 2x^2y^2 +y^4 = 16.$$

Find the Cartesian equation for the curve $$ r = \tan \theta + \sec \theta.$$

Derivatives:

Find $dy/dx$ for the following curves:

$$x^4 + 2x^2y^2 +y^4 = 16$$

$$ r = \tan \theta + \sec \theta.$$

Intersections:

Find the points of intersection of the curves $r(t) = \cot \theta$ and $s(t) = 2 \cos \theta$.

Challenge:

Show that if $m$ is any real number, then there are exactly two lines of slope $m$ that are tangent to the ellipse $$x^2/a^2+y^2/b^2 = 1$$ and their equations are $$y = mx \pm \sqrt{a^2 m^2+b^2}.$$