91Ó°ÊÓ

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. \(x\)-intercepts \(\pm 5, \quad\) asymptotes \(y=\pm 2 x\)

Exer. 27-44: Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. Use it to help sketch the graph in an \(r \theta\)-plane. $$ r-6 \sin \theta=0 $$

Exer. 25-32: Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix. $$ e=1, \quad r \sin \theta=-2 $$

Exer. 19-30: Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. Horizontal major axis of length 8 , minor axis of length 5

Exer. 19-30: Find an equation of the parabola that satisfies the given conditions. Vertex \(V(-3,5)\), axis parallel to the \(x\)-axis, and passing through the point \((5,9)\)

Exer. 19-30: Find an equation for the ellipse that has its center at the origin and satisfies the given conditions. Vertical major axis of length 7 , minor axis of length 6

Exer. 19-30: Find an equation of the parabola that satisfies the given conditions. Vertex \(V(3,-2)\), axis parallel to the \(x\)-axis, and \(y\)-intercept 1

Exer. 25-32: Find a polar equation of the conic with focus at the pole that has the given eccentricity and equation of directrix. $$ e=4, \quad r=-3 \csc \theta $$

Exer. 27-44: Find an equation in \(x\) and \(y\) that has the same graph as the polar equation. Use it to help sketch the graph in an \(r \theta\)-plane. $$ r=2 $$

Find an equation for the hyperbola that has its center at the origin and satisfies the given conditions. \(y\)-intercepts \(\pm 2, \quad\) asymptotes \(y=\pm \frac{1}{4} x\)