91Ó°ÊÓ

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. $$(5.4,2.85)$$

Sketching an Ellipse In Exercises \(33-48,\) find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$(x+2)^{2}+\frac{(y+4)^{2}}{1 / 4}=1$$

Graphing a Curve In Exercises \(35-46,\) use a graphing utility to graph the curve represented by the parametric equations. $$ \begin{array}{l}{x=|t+2|} \\ {y=3-t}\end{array} $$

Rotation and Graphing Utilities In Exercises \(37 - 44 , (\) a) use the discriminant to classify the graph of the equation, (b) use the Quadratic Formula to solve for \(y\) and (c) use a graphing utility to graph the equation. $$ 2 x ^ { 2 } + 4 x y + 5 y ^ { 2 } + 3 x - 4 y - 20 = 0 $$

Finding the Vertex, Focus, and Directrix of a Parabola In Exercises \(29-42,\) find the vertex, focus, and directrix of the parabola. Then sketch the parabola. $$x=\frac{1}{4}\left(y^{2}+2 y+33\right)$$

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

Finding the Standard Equation, find the standard form of the equation of the hyperbola with the given characteristics. $$ \text { Foci: }(0, \pm 8) ; \text { asymptotes: } y=\pm 4 x $$

Find a polar equation of the conic with its focus at the pole. Conic \(\quad\) Eccentricity \(\quad\) Directrix Ellipse \(\quad e=\frac{1}{2} \quad y=1\)

Find the inclination \(\theta\) (in radians and degrees) of the line. \(6 x-2 y+8=0\)

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. $$(-4.1,-0.5)$$