91Ó°ÊÓ

Finding the Standard Equation, find the standard form of the equation of the hyperbola with the given characteristics. $$ \text { Vertices: }(\pm 1,0) ; \text { asymptotes: } y=\pm 5 x $$

Find the inclination \(\theta\) (in radians and degrees) of the line. \(x+\sqrt{3} y+2=0\)

Sketching an Ellipse In Exercises \(33-48,\) find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$\frac{(x+5)^{2}}{9 / 4}+(y-1)^{2}=1$$

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. $$y=\frac{1}{4}\left(x^{2}-2 x+5\right)$$

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. $$(2.5,1.58)$$

Graphing a Curve In Exercises \(35-46,\) use a graphing utility to graph the curve represented by the parametric equations. $$ \begin{array}{l}{x=2 t} \\ {y=|t+1|}\end{array} $$

Finding the Standard Equation, find the standard form of the equation of the hyperbola with the given characteristics. $$ \text { Vertices: } (0, \pm 3) ; \text { asymptotes: } y=\pm 3 x $$

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

Find a polar equation of the conic with its focus at the pole. Conic \(\quad\) Eccentricity \(\quad\) Directrix Parabola \(\quad e=1 \quad y=-4\)

Find the inclination \(\theta\) (in radians and degrees) of the line. \(-2 \sqrt{3} x-2 y=0\)