91Ó°ÊÓ

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. $$r=8 \cos \theta$$

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

Finding the Standard Equation of a Parabola In Exercises \(47-56\) , find the standard form of the equation of the parabola with the given characteristics. $$(1,2) \text { ; directrix: } y=-1$$

In Exercises 49-58, use a graphing utility to graph the polar equation. Describe your viewing window. $$r=\cos 2 \theta$$

Find the angle \(\theta\) (in radians and degrees) between the lines. \(0.02 x-0.05 y=-0.19\) \(0.03 x+0.04 y \quad =0.52\)

Classifying a Conic from a General Equation, classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$ x^{2}+y^{2}-4 x-6 y-23=0 $$

Using Eccentricity Find an equation of the ellipse with vertices \((0, \pm 8)\) and eccentricity \(e=\frac{1}{2} .\)

Sketching the Graph of a Degenerate Conic In Exercises \(45 - 54\) , sketch (if possible) the graph of the degenerate conic. $$ x ^ { 2 } + y ^ { 2 } - 2 x + 6 y + 10 = 0 $$

Classifying a Conic from a General Equation, classify the graph of the equation as a circle, a parabola, an ellipse, or a hyperbola. $$ 4 x^{2}-y^{2}-4 x-3=0 $$

Finding the Standard Equation of a Parabola In Exercises \(47-56\) , find the standard form of the equation of the parabola with the given characteristics. $$(2,2) ; \text { directrix: } x=-2$$