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. $$x=t^{3}, \quad y=t^{2};\quad t \text { in } \mathbb{R}$$

Find an equation of the parabola that satisfies the given conditions. Vertex \(V(4,2), \quad\) directrix \(y=-6\)

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. Vertices \(V(0, \pm 12),\) passing through \((5,13)\)

Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix. $$e=1, r \sin \theta=-2$$

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

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. Vertices \(V(\pm 3,0), \quad\) asymptotes \(y=\pm 2 x\)

Exer \(19-36:\) Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. Eccentricity \(\frac{3}{4}\) vertices \(H 0, \pm 4)\)

Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix. $$e=4, \quad r=-3 \csc \theta$$

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=\tan t, \quad y=1 ; \quad-\pi / 2

Find an equation of the parabola that satisfies the given conditions. $$\text { Vertex }M-2,1), \quad \text { focus } F(2,1)$$