91Ó°ÊÓ

Find the standard form of the equation of the ellipse with the given characteristics. $$\text { Center: }(0,2) ; a=4 c ; \text { vertices: }(0,-6),(0,10)$$

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. $$(-\sqrt{3},-1),(0,-2)$$

Use a graphing utility to graph the polar equation. Identify the graph. $$r=\frac{-1}{1-\sin \theta}$$

Find the standard form of the equation of the parabola with the given characteristic(s) and vertex at the origin. Horizontal axis and passes through the point (-2,5)

Sketch the graph of the polar equation using symmetry, zeros, maximum \(r\) -values, and any other additional points. $$r=\sin \theta$$

A point in polar coordinates is given. Convert the point to rectangular coordinates. $$(-2,7 \pi / 6)$$

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. Then sketch the hyperbola using the asymptotes as an aid. $$\frac{(y+6)^{2}}{1 / 9}-\frac{(x-2)^{2}}{1 / 4}=1$$

Use a graphing utility to graph the polar equation. Identify the graph. $$r=\frac{-5}{2+4 \sin \theta}$$

Use a graphing utility to graph the conic. Determine the angle 8 through which the axes are rotated. Explain how you used the graphing utility to obtain the graph. $$24 x^{2}+18 x y+12 y^{2}=34$$

Find the inclination \(\theta\) (in radians and degrees) of the line passing through the points. $$(3, \sqrt{3}),(6,-2 \sqrt{3})$$