91Ó°ÊÓ

Find polar equations for the circles in Exercises \(13-16\) Radius \(=\sqrt{2}\)

Graph the lemniscates in Exercises \(13-16 .\) What symmetries do these curves have? $$ r^{2}=-\cos 2 \theta $$

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises \(7-22\) . $$ \theta=\pi / 2, \quad r \geq 0 $$

Use the discriminant \(B^{2}-4 A C\) to decide whether the equations represent parabolas, ellipses, or hyperbolas. \(6 x^{2}+3 x y+2 y^{2}+17 y+2=0\)

Find the areas of the regions Inside the circle \(r=6\) above the line \(r=3 \csc \theta\)

Find the areas of the regions Inside the lemniscate \(r^{2}=6 \cos 2 \theta\) to the right of the line \(r=(3 / 2) \sec \theta\)

Graph the sets of points whose polar coordinates satisfy the equations and inequalities in Exercises \(7-22\) . $$ \theta=\pi / 2, \quad r \leq 0 $$

Trochoids A wheel of radius \(a\) rolls along a horizontal straight line without slipping. Find parametric equations for the curve traced out by a point \(P\) on a spoke of the wheel \(b\) units from its center. As parameter, use the angle \(\theta\) through which the wheel turns. The curve is called a trochoid, which is a cycloid when \(b=a\).

Graph the lemniscates in Exercises \(13-16 .\) What symmetries do these curves have? $$ r^{2}=-\sin 2 \theta $$

Use the discriminant \(B^{2}-4 A C\) to decide whether the equations represent parabolas, ellipses, or hyperbolas. \(3 x^{2}+12 x y+12 y^{2}+435 x-9 y+72=0\)