91Ó°ÊÓ

When a plane passes through the vertex of a double-napped cone, the intersection is a______________ ______________.

Sketching a Curve In Exercises \(7-34,\) (a) sketch the curve represented by the parametric equations (indicate the orientation of the curve) and (b) eliminate the parameter and write the resulting rectangular equation whose graph represents the curve. Adjust the domain of the rectangular equation, if necessary. $$ \begin{array}{l}{x=3-2 t} \\ {y=2+3 t}\end{array} $$

An Ellipse Centered at the Origin In Exercises \(9-18\) , find the standard form of the equation of the ellipse with the given characteristics and center at the origin. Vertices: \((0, \pm 5) ;\) passes through the point \((4,2)\)

Rotation of Axes In Exercises \(13 - 24 ,\) rotate the axes to eliminate the \(x y\) -term in the equation. Then write the equation in standard form. Sketch the graph of the resulting equation, showing both sets of axes. $$ x ^ { 2 } + 2 x y + y ^ { 2 } + \sqrt { 2 } x - \sqrt { 2 } y = 0 $$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=\sin \theta$$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=2(1+\cos \theta)$$

Polar-to-Rectangular Conversion In Exercises \(19-34\) , a point in polar coordinates is given. Convert the point to rectangular coordinates. $$(-2,5.76)$$

Using a Graphing Utility to Find Rectangular Coordinates In Exercises \(35-42,\) use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(8.25,3.5)$$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=3+6 \sin \theta$$

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=6 \cos 3 \theta$$