91Ó°ÊÓ

For the following exercises, find the slope of the tangent line to the given polar curve at the point given by the value of \(\theta\) \(r=\ln \theta, \quad \theta=e\)

For the following exercises, find the slope of the tangent line to the given polar curve at the point given by the value of \(\theta\) [T] Use technology: \(r=2+4 \cos \theta\) at \(\theta=\frac{\pi}{6}\)

For the following exercises, find the points at which the following polar curves have a horizontal or vertical tangent line. \(r=4 \cos \theta\)

For the following exercises, find the points at which the following polar curves have a horizontal or vertical tangent line. \(r=2 \sin (2 \theta)\)

For the following exercises, find the points at which the following polar curves have a horizontal or vertical tangent line. The cardioid \(r=1+\sin \theta\)

Show that the curve \(r=\sin \theta \tan \theta\) (called a cissoid of Diocles) has the line \(x=1\) as a vertical asymptote.

For the following exercises, determine the equation of th parabola using the information given. Focus \((4,0)\) and directrix \(x=-4\)

For the following exercises, determine the equation of the parabola using the information given. Focus \((0,-3)\) and directrix \(y=3\)

For the following exercises, determine the equation of the parabola using the information given. Focus \((0,0.5)\) and directrix \(y=-0.5\)

For the following exercises, determine the equation of the parabola using the information given. Focus (2,3) and directrix \(x=-2\)