91Ó°ÊÓ

A point in rectangular coordinates is given. Convert the point to polar coordinates. $$(-6,0)$$

Find the angle \(\theta\) (in radians and degrees) between the lines. $$\begin{array}{rr} x-y= & 0 \\ 3 x-2 y= & -1 \end{array}$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc}\text{Conic} & \text{Vertex or Vertices} \\\ \text{Parabola} & (5, \pi) \end{array}$$

Find the center, vertices, foci, and eccentricity of the ellipse. Then sketch the ellipse. $$16 x^{2}+25 y^{2}-32 x+50 y+16=0$$

Sketch the graph of the polar equation using symmetry, zeros, maximum \(r\) -values, and any other additional points. $$r^{2}=9 \cos 2 \theta$$

Determine how the plane curves differ from each other. (a) \(x=t\) \(y=2 t+1\) (b) \(x=\cos \theta\) \(y=2 \cos \theta+1\) (c) \(x=e^{-t}\) \(y=2 e^{-t}+1\) (d) \(x=e^{t}\) \(y=2 e^{t}+1\)

A point in rectangular coordinates is given. Convert the point to polar coordinates. $$(3,0)$$

Determine how the plane curves differ from each other. (a) \(x=t$$y=t^{2}-1\) (b) \(x=t^{2}$$y=t^{4}-1\) (c) \(x=\sin t$$y=\sin ^{2} t-1\) (d) \(x=e^{t}$$y=e^{2 t}-1\)

Find the angle \(\theta\) (in radians and degrees) between the lines. $$\begin{aligned} &2 x-y=2\\\ &4 x+3 y=24 \end{aligned}$$

Find a polar equation of the conic with its focus at the pole. $$\begin{array}{cc}\text{Conic} & \text{Vertex or Vertices} \\\ \text{Parabola} & (10, \pi / 2) \end{array}$$