91Ó°ÊÓ

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(5, 12\right)\)

In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Hypocycloid: \(\quad x= 3 \cos^{3}\ \theta, \quad y= 3 \sin^{3}\ \theta\)

In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Curtate cycloid: \(\quad x= 8\theta - 4 \sin\ \theta, \quad y= 8 - 4 \cos\ \theta\)

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. \(r=\cos\ 2\theta\)

In Exercises 39-54, find a polar equation of the conic with its focus at the pole. \(\textit{Conic}\) Hyperbola \(\textit{Vertex or Vertices}\) \((4, \pi/2), (1, \pi/2)\)

In Exercises 51-56, sketch (if possible) the graph of the degenerate conic. \(5x^2-2xy+5y^2=0\)

In Exercises 37-54, a point in rectangular coordinates is given. Convert the point to polar coordinates. \(\left(7, 15\right)\)

In Exercises 51-58, find the distance between the point and the line. \(\textit{Point}\) \((-2, 1)\) \(\textit{Line}\) \(x - y = 2\)

In Exercises 51-60, find the standard form of the equation of the parabola with the given characteristics. Vertex: \((4, 3) \quad\) focus: \((6, 3)\)

In Exercises 49-56, use a graphing utility to graph the curve represented by the parametric equations. Witch of Agnesi: \(\quad x= 2 \cot\ \theta, \quad y= 2 \sin^{2}\ \theta\)