In Exercises 1–8, sketch the graph of each parabola. Determine the vertex, focus, axis, and directrix of each parabola.
In Exercises 9–12, find an equation of the parabola satisfying the given conditions.
Vertex: (0, 0) focus:
Vertex: (0, 0) focus: (0, 4)
Focus: (0, 4) directrix:
Focus:
In Exercises 13–20, sketch the graph of each ellipse. Determine the foci, vertices, and endpoints of the minor axis of the ellipse.
In Exercises 21–24, find an equation of the ellipse satisfying the given conditions.
Vertices:
Vertices:
Length of major axis: 20; foci:
Length of minor axis: 16; foci:
In Exercises 25–32, sketch the graph of each hyperbola. Determine the vertices, the foci, and the asymptotes of each hyperbola.
In Exercises 33–36, find an equation of the hyperbola satisfying the given condition.
Vertices:
Vertices:
Vertices:
Vertices:
In Exercises 37–48, identify each equation as representing a circle, a parabola, an ellipse, or a hyperbola. Sketch the graph of the conic.
Find an equation of the hyperbola whose foci are the vertices of the ellipse
Find an equation of the ellipse whose foci are the vertices of the hyperbola
In Exercises 51–54, find all points of intersection of the given curves and make a sketch.
Parabolic curve. Water flowing from the end of a horizontal pipe 20 feet above the ground describes a parabolic curve whose vertex is at the end of the pipe. If at a point 6 feet below the line of the pipe the flow of water has curved outward 8 feet beyond a vertical line through the end of the pipe, how far beyond this vertical line will the water strike the ground?
Parabolic arch. A parabolic arch has a height of 20 meters and a width of 36 meters at the base. Assuming that the vertex of the parabola is at the top of the arch, find the height of the arch at a distance of 9 meters from the center of the base.
Football. A football is 12 inches long, and a cross section containing a seam is an ellipse with a minor axis of length 7 inches. Suppose every cross section of the ball formed by a plane perpendicular to the major axis of the ellipse is a circle. Find the circumference of such a circular cross section located 2 inches from an end of the ball.
Production cost. A company assembles computers at two locations A and B that are 1000 miles apart. The per unit cost of production at location A is $20 less than at location B. Assume that the route of delivery of the computers is along a straight line and that the delivery cost is
[Hint: Take A at