91Ó°ÊÓ

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=\sin t, \quad y=\csc t ; \quad 0

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. \(x=e^{t}, \quad y=e^{-t}\) \(t\) in \(\mathrm{R}\)

Find a polar equation that has the same graph as the equation in \(x\) and \(y\). $$x^{2}+y^{2}=2$$

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$25 x^{2}-9 y^{2}+100 x-54 y+10=0$$

Find a polar equation that has the same graph as the equation in \(x\) and \(y\). $$y^{2}=6 x$$

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=t, \quad y=\sqrt{t^{2}-1} ; \quad|t| \geq 1$$

Find a polar equation that has the same graph as the equation in \(x\) and \(y\). $$x^{2}=8 y$$

Find an equation in \(x\) and \(y\) whose graph contains the points on the curve \(C\). Sketch the graph of \(C\), and indicate the orientation. $$x=-2 \sqrt{1-t^{2}}, y=t ; \quad|t| \leq 1$$

Find a polar equation that has the same graph as the equation in \(x\) and \(y\). $$x+y=3$$

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. $$\text { Vertices } V(\pm 8,0), \quad \text { foci } F(\pm 5,0)$$