Two adjoining square fields with an area of 2900 square feet are to be enclosed with 240

In Exercises 12, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places.(-2, -3) and (3, 9)

In Exercises 12, find the distance between each pair of points. If necessary, express answers in simplified radical form and then round to two decimal places.(-4, 3) and (-2, 5)

In Exercises 34, find the midpoint of the line segment with the given endpoints.(2, 6) and (-12, 4)

In Exercises 34, find the midpoint of the line segment with the given endpoints.(4, -6) and (-15, 2)

In Exercises 56, write the standard form of the equation of the circle with the given center and radius.Center (0, 0), r = 3

In Exercises 56, write the standard form of the equation of the circle with the given center and radius.Center (-2, 4), r = 6

In Exercises 710, give the center and radius of each circle and graph its equation.x2 + y2 = 1

In Exercises 710, give the center and radius of each circle and graph its equation.(x + 2) 2 + (y - 3) 2 = 9

In Exercises 710, give the center and radius of each circle and graph its equation.x2 + y2 - 4x + 2y - 4 = 0

In Exercises 710, give the center and radius of each circle and graph its equation.x2 + y2 - 4y = 0

In Exercises 1116, graph each ellipsex2 36 + y2 25 = 1

In Exercises 1116, graph each ellipsex2 25 + y2 16 = 1

In Exercises 1116, graph each ellipse 4x2 + y2 = 16

In Exercises 1116, graph each ellipse 4x2 + 9y2 = 36

In Exercises 1116, graph each ellipse (x - 1) 2 16 + (y + 2) 2 9 = 1

In Exercises 1116, graph each ellipse (x + 1) 2 9 + (y - 2) 2 16 = 1

A semielliptic archway has a height of 15 feet at the center and a width of 50 feet, as shown in the figure. The 50-foot width consists of a two-lane road. Can a truck that is 12 feet high and 14 feet wide drive under the archway without going into the other lane? 50 feet 15 feet 12 feet 14 feet

In Exercises 1821, use vertices and asymptotes to graph each hyperbola.x2 16 - y2 = 1

In Exercises 1821, use vertices and asymptotes to graph each hyperbola.y2 16 - x2 = 1

In Exercises 1821, use vertices and asymptotes to graph each hyperbola.9x2 - 16y2 = 144

In Exercises 1821, use vertices and asymptotes to graph each hyperbola.4y2 - x2 = 16

In Exercises 2225, use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry.x = (y - 3) 2 - 4

In Exercises 2225, use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry.x = -2(y + 3) 2 + 2

In Exercises 2225, use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry.x = y2 - 8y + 12

In Exercises 2225, use the vertex and intercepts to sketch the graph of each equation. If needed, find additional points on the parabola by choosing values of y on each side of the axis of symmetry.x = -y2 - 4y + 6

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola x + 8y = y2 + 10

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola 16x2 = 32 - y2

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabolax2 = 25 + 25y2

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabolax2 = 4 - y2

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola 36y2 = 576 + 16x2

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola (x + 3) 2 9 + (y - 4) 2 25 = 1

In Exercises 2632, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola y = x2 + 6x + 9

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.5x2 + 5y2 = 180

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.4x2 + 9y2 = 36

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.4x2 - 9y2 = 36

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.x2 25 + y2 1 = 1

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.x + 3 = -y2 + 2y

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.y - 3 = x2 - 2x

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.(x + 2) 2 16 + (y - 5) 2 4 = 1

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.(x - 3) 2 + (y + 2) 2 = 4

In Exercises 3341, indicate whether the graph of each equation is a circle, an ellipse, a hyperbola, or a parabola. Then graph the conic section.x2 + y2 + 6x - 2y + 6 = 0

An engineer is designing headlight units for automobiles. The unit has a parabolic surface with a diameter of 12 inches and a depth of 3 inches. The situation is illustrated in the figure, where a coordinate system has been superimposed. 3 inches 12 inches y x Vertex (0, 0) (6, 3) 6 6 a. Use the point (6, 3) to write an equation in the form y = ax2 for the parabola used to design the headlight. b. The light source should be placed at the focus (0, p). The value of p is given by the equation a = 1 4p . Where should the light source be placed? Describe this placement relative to the vertex.

In Exercises 4353, solve each system by the method of your choice.e 5y = x2 - 1 x - y = 1

In Exercises 4353, solve each system by the method of your choice.e y = x2 + 2x + 1 x + y = 1

In Exercises 4353, solve each system by the method of your choice.e x2 + y2 = 2 x + y = 0

In Exercises 4353, solve each system by the method of your choice.e 2x2 + y2 = 24 x2 + y2 = 15

In Exercises 4353, solve each system by the method of your choice.e xy - 4 = 0 y - x = 0

In Exercises 4353, solve each system by the method of your choice.e y2 = 4x x - 2y + 3 = 0

In Exercises 4353, solve each system by the method of your choice.e x2 + y2 = 10 y = x + 2

In Exercises 4353, solve each system by the method of your choice.e xy = 1 y = 2x + 1

In Exercises 4353, solve each system by the method of your choice.e x + y + 1 = 0 x2 + y2 + 6y - x = -5

In Exercises 4353, solve each system by the method of your choice.e x2 + y2 = 13 x2 - y = 7

In Exercises 4353, solve each system by the method of your choice.e 2x2 + 3y2 = 21 3x2 - 4y2 = 23

The perimeter of a rectangle is 26 meters and its area is 40 square meters. Find its dimensions.

Find the coordinates of all points (x, y) that lie on the line whose equation is 2x + y = 8, so that the area of the rectangle shown in the figure is 6 square units. y x x y (x, y) 2x + y = 8

Two adjoining square fields with an area of 2900 square feet are to be enclosed with 240 feet of fencing. The situation is represented in the figure. Find the length of each side where a variable appears. x x y y