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Wading Pool You are building a wading pool that is in the shape of an ellipse. An equation for the elliptical shape of the pool is
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- An arch has the shape of a semi-ellipse. The arch has a height of 12 feet and a span of 40 feet. Find an equation for the ellipse, and use that to find the distance from the center to a point at which the height is 6 feet. Round to the nearest hundredth.arrow_forwardAn arch has the shape of a semi-ellipse (the top half of an ellipse). The arch has a height of 8 feet and a span of 20 feet. Find an equation for the ellipse, and use that to find the height to the nearest 0.01 foot of the arch at a distance of 4 feet from the center.arrow_forwardProjectiles The cannonball in the illustration follows the parabolic trajectory y=30xx2. How far short of the castle does it land?arrow_forward
- The filament of a light bulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends light out in a straight beam. Given that the filament is 1.5 inches from the vertex, find an equation for the cross section of the reflector. The reflector is 7 inches wide. How deep is it? The filament of a light bulb is a thin wire that glows when electricity passes through it. The filament of a car headlight is at the focus of a parabolic reflector, which sends light out in a straight beam. Given that the filament is 1.5 inches from the vertex, find an equation for the cross section of the reflector. The reflector is 7 inches wide. How deep is it?arrow_forwardSonic boom The position of a sonic boom caused by the faster-than-sound aircraft is one branch of the hyperbola y2x2=25 in the coordinate system shown. How wide is the hyperbola 5 miles from its vertex?arrow_forwardSatellite antennas The cross section of the satellite antenna in the illustration is a parabola given by the equation y=116x2, with distance measured in feet. If the dish is 8feet wide, how deep it is?arrow_forward
- The light bulb in a flashlight is at the focus of the parabolic reflector, 1.5 centimeters from the vertex of the reflector (see figure). Write an equation for a cross section of the flashlight’s reflector with its focus on the positive x-axis and its vertex at the origin.arrow_forwardBeam Deflection A simply supported beam (see figure) is 64 feet long and has a load at the center. The deflection of the beam at its center is 1 inch. The shape of the deflected beam is parabolic. (a) Write an equation of the parabola. (Assume that the origin is at the center of the beam.) (b) How far from the center of the beam is the deflection 12 inch?arrow_forwardSuspension Bridge In a suspension bridge the shape of the suspension cables is parabolic. The bridge shown in the figure has towers that are 600 m apart, and the lowest point of the suspension cables is 150 m below the top of the towers. Find the equation of the parabolic part of the cables, placing the origin of the coordinate system at the vertex. [Note: This equation is used to find the length of cable needed in the construction of the bridge.]arrow_forward
- Road Design Roads are often designed with parabolic surfaces to allow rain to drain off. A particular road is 32 feet wide and 0.4 foot higher in the center than it is on the sides (see figure). (a) Write an equation of the parabola with its vertex at the origin that models the road surface. (b) How far from the center of the road is the road surface 0.1 foot lower than the center?arrow_forwardThe receiver of a parabolic satellite dish is at the focus of the parabola (see figure). Write an equation for a cross section of the satellite dish.arrow_forwardStatuary Hall is an elliptical room in the United States Capitol in Washington, D.C. The room is also called the Whispering Gallery because a person standing at one focus of the room can hear even a whisper spoken by a person standing at the other focus. This occurs because any sound emitted from one focus of an ellipse reflects off the side of the ellipse to the other focus. Statuary Hall is 46 feet wide and 97 feet long. (a) Find an equation that models the shape of the room. (b) How far apart are the two foci? (c) What is the area of the floor of the room? (The area of an ellipse is A=ab.)arrow_forward
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