Applications of Conics Answers

A castle entrance has walls that can be modeled by the equation with units in feet. How wide is the entrance where the walls are closest together?

A cooling tower is 120 meters tall. The sides of the tower are in the shape of a hyperbola defined by the equation with units in meters. The center of the tower is at the origin. How wide is the tower at the top?

A mirror is the shape of an ellipse defined by with units in feet. Which statement identifies the orientation of the mirror and its greatest dimension?

A carpenter designs a tabletop in the shape of an ellipse 7 feet long and 4 feet wide. The carpenter sketches a drawing of the tabletop on a coordinate plane. The center of the tabletop is at the origin, the length falls along the x-axis, and the width falls along the y-axis. Which equation represents the tabletop?

Lori tosses a ball into the air. The equation y = –16(x – 1)2 + 25 models the height, y, in feet, of the ball after x seconds. What is the maximum height the ball reaches?

A garden has the shape of an ellipse. Review the table of values that shows several points on the fence of the garden. The positive y-axis represents due north.x(in feet)y(in feet)–1440015014400–150

A pair of radar stations monitors the path of a helicopter. Station A is located at the origin of a coordinate plane. Station B is located 100 miles east of station A. The difference in the distances from the helicopter to each station is 60 miles. Which equation represents the possible locations of the helicopter?

A serving dish has a parabolic surface with the vertex (0, 0) at the center of the dish. When the width of the dish is 6 inches, the depth of the dish is 3 inches. The equation that models the shape of the serving dish is y = ax2. What is the value of a?

Antonio constructs a model of a moon orbiting a planet along an elliptical orbit. The equation , with units in inches, represents the shape of the orbit. If the planet is located at one of the foci, which phrase describes a possible location of the model planet relative to the center?

Ailani draws a map of her local town. She places the town hall at the origin of a coordinate plane and represents a lake with a circle drawn on the map. The center of the lake is 19 miles east and 3 miles south of the town hall, and the radius of the lake is 0.5 miles.If the positive x-axis represents east and the positive y-axis represents north, which equation represents the lake?