91Ó°ÊÓ

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(4,11 \pi / 9)$$

Use a graphing utility to find the rectangular coordinates of the point given in polar coordinates. Round your results to two decimal places. $$(-4.5,1.3)$$

Find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$\frac{(x-4)^{2}}{16}+\frac{(y+1)^{2}}{25}=1$$

Find the center, vertices, foci, and the equations of the asymptotes of the hyperbola. Use a graphing utility to graph the hyperbola and its asymptotes. $$9 y^{2}-x^{2}+2 x+54 y+62=0$$

(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. $$16 x^{2}-8 x y+y^{2}-10 x+5 y=0$$

Use a graphing utility to graph the curve represented by the parametric equations. $$\begin{aligned} &x=t\\\ &y=\sqrt{t} \end{aligned}$$

Find the inclination \(\theta\) (in radians and degrees) of the line. $$3 x-3 y+1=0$$

Use a graphing utility to graph the rotated conic. $$r=\frac{6}{2+\sin (\theta+\pi / 6)}$$

Sketch the graph of the polar equation using symmetry, zeros, maximum \(r\) -values, and any other additional points. $$r=2-4 \cos \theta$$

Find the vertex, focus, and directrix of the parabola. Then sketch the parabola. $$(x+3)^{2}=4\left(y-\frac{3}{2}\right)$$