91Ó°ÊÓ

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

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. $$ x ^ { 2 } - 6 x y - 5 y ^ { 2 } + 4 x - 22 = 0 $$

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

Sketching an Ellipse In Exercises \(33-48,\) find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$9 x^{2}+4 y^{2}+36 x-24 y+36=0$$

Finding the Standard Equation, find the standard form of the equation of the hyperbola with the given characteristics. $$ \text { Foci: } (\pm 10,0) ; \text { asymptotes: } y=\pm \frac{3}{4} x $$

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

Find the inclination \(\theta\) (in radians and degrees) of the line. \(2 x-6 y-12=0\)

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. $$(8.2,-3.2)$$

Graphing a Curve In Exercises \(35-46,\) use a graphing utility to graph the curve represented by the parametric equations. $$ \begin{array}{l}{x=4+3 \cos \theta} \\ {y=-2+2 \sin \theta}\end{array} $$

Sketching an Ellipse In Exercises \(33-48,\) find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$9 x^{2}+4 y^{2}-54 x+40 y+37=0$$