91Ó°ÊÓ

Find the vertices and foct of the ellipse. Sketch Its graph, showing the foci. $$25 x^{2}+4 y^{2}-250 x-16 y+541=0$$

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

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$144 x^{2}-25 y^{2}+864 x-100 y-2404=0$$

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. $$x=t^{2}, \quad y=2 \ln t ; \quad t>0$$

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

Find the vertices and foct of the ellipse. Sketch Its graph, showing the foci. $$4 x^{2}+y^{2}=2 y$$

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. $$\begin{aligned}&x=\cos ^{3} t, \quad y=\sin ^{3} t&0 \leq t \leq 2 \pi\end{aligned}$$

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$y^{2}-4 x^{2}-12 y-16 x+16=0$$

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=\sin t, \quad y=\csc t ; \quad 0

Find the vertices, the focl, and the equations of the asymptotes of the hyperbola. Sketch its graph, showing the asymptotes and the foci. $$4 y^{2}-x^{2}+40 y-4 x+60=0$$