91Ó°ÊÓ

Find a polar equation that has the same graph as the equation in \(x\) and \(y\). $$x=5$$

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. $$x=\cos t, \quad y=\cos 2 t, \quad-\pi \leq t \leq \pi$$

Find the vertices, the foci, 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 \(y\). $$x^{2}+y^{2}=16$$

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

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

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

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

Exer \(19-36:\) Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. $$\text { Vertices }V \pm 8,0), \quad \text { foci } F(\pm 5,0)$$

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