91Ó°ÊÓ

Find the polar equation of the conic section that has focus (0,0) and satisfies the given conditions. Hyperbola; vertical directrix to the left of the pole; eccentricity \(2 ;(1,2 \pi / 3)\) is on the graph.

Find the equation of the ellipse that satisfies the given conditions. Center (2,3)\(;\) endpoints of major and minor axes: (2,-1), (0,3),(2,7),(4,3).

Find a rectangular equation that is equivalent to the given polar equation. \(r=\sec \theta[\text {Hint}:\) Express the right side in terms of cosine.]

Use Exercise 44 to find a parameterization of the line segment joining the two points. Confirm your answer by graphing. $$(-6,12) \text { and }(12,-10)$$

In Exercises \(43-54\), find the equation of the parabola satisfying the given conditions. Vertex (1,0)\(;\) axis \(x=1 ;(2,13)\) on graph.

Find the equation of the ellipse that satisfies the given conditions. Center (-5,2)\(;\) endpoints of major and minor axes: (0,2), (-5,17),(-10,2),(-5,-13).

Use Exercise 44 to find a parameterization of the line segment joining the two points. Confirm your answer by graphing. $$(14,-5) \text { and }(5,-14)$$

Find the polar equation of the conic section that has focus (0,0) and satisfies the given conditions. Hyperbola; horizontal directrix above the pole; eccentricity \(2 ;(1,2 \pi / 3)\) is on the graph.

In Exercises \(43-54\), find the equation of the parabola satisfying the given conditions. Vertex (-3,0)\(;\) axis \(y=0 ;(-1,1)\) on graph.

Find the equation of the ellipse that satisfies the given conditions. Center (7,-4)\(;\) foci on the line \(x=7 ;\) major axis of length \(12 ;\) minor axis of length 5.