91Ó°ÊÓ

Finding the Vertex, Focus, and Directrix of a Parabola In Exercises \(43-46,\) find the vertex, focus, and directrix of the parabola. Use a graphing utility to graph the parabola. $$x^{2}-2 x+8 y+9=0$$

Sketching an Ellipse In Exercises \(33-48,\) find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$3 x^{2}+y^{2}+18 x-2 y-8=0$$

Finding the Standard Equation, find the standard form of the equation of the hyperbola with the given characteristics. $$ \begin{array}{l}{\text { Vertices: }(3,0),(3,6) ;} \\ {\text { asymptotes: } y=6-x, y=x}\end{array} $$

Rectangular-to-Polar Conversion In Exercises \(43-60,\) a point in rectangular coordinates is given. Convert the point to polar coordinates. $$(2,2)$$

Find the inclination \(\theta\) (in radians and degrees) of the line. \(5 x+3 y=0\)

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

Find a polar equation of the conic with its focus at the pole. Conic \(\quad\) Eccentricity \(\quad\) Directrix Hyperbola \(\quad e=\frac{3}{2} \quad x=-1\)

In Exercises \(23-48\) , sketch the graph of the polar equation using symmetry, zeros, maximum r-values, and any other additional points. $$r=5 \csc \theta$$

Rectangular-to-Polar Conversion In Exercises \(43-60,\) a point in rectangular coordinates is given. Convert the point to polar coordinates. $$(-3,-3)$$

Find the angle \(\theta\) (in radians and degrees) between the lines. \(3 x+y=3\) \(x-y=2\)