Applications of Conics Answers

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?

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 company produces circular drink coasters. The equation x2 + y2 = 18.0625, with units in inches, represents the size of a coaster. Each coaster is cut from a square piece of cardboard. What is the minimum possible area of each cardboard piece?

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?

A drone has an effective range represented by a circle on a coordinate plane. The points (–12, 3) and (–6, –5) are endpoints of a diameter of this boundary. Which equation represents the effective range boundary for the drone?

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 company is introducing a new product. The equation y = –0.001(x – 600)2 + 90 predicts the expected profit, in thousands of dollars, where x represents the number of thousands of units of the product sold by the company. How many units must be sold to yield a maximum profit?

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 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 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