Exploring Conic Sections: Real-Life Applications in Geometry

A gardener wants to design a circular flower bed with a radius of 3 meters. What is the equation of the circle in standard form?

• x² + y² = 9

• x² + y² = 6

• x² + y² = 12

• x² + y² = 3

A satellite dish is shaped like a parabola. If the focus is located 2 feet from the vertex, what is the equation of the parabola if it opens upwards?

• y² = 8x

• x² = 4y

• x² = -8y

• x² = 8y

A car is traveling along a path that can be modeled by the equation of an ellipse, given by (x^2/16) + (y^2/9) = 1. Identify the lengths of the major and minor axes.

• Major axis length: 6, Minor axis length: 8

• Major axis length: 10, Minor axis length: 4

• Major axis length: 12, Minor axis length: 5

• Major axis length: 8, Minor axis length: 6

A basketball hoop is 10 feet high and the ball follows a parabolic path. If the vertex of the parabola is at (0, 10) and it passes through the point (5, 0), what is the equation of the parabola?

• y = -x^2 + 5

• y = -2/5x^2 + 10

• y = 2/5x^2 + 10

• y = 1/2x^2 + 10

An architect is designing a building with a circular dome. If the dome has a diameter of 20 meters, what is the equation of the circle that represents the base of the dome?

• (x)² + (y)² = 200

• (x - 10)² + (y - 10)² = 100

• (x)² + (y)² = 100

• (x)² + (y)² = 50

A roller coaster track is shaped like a hyperbola. If one of the foci is located at (0, 5) and the other at (0, -5), what is the equation of the hyperbola?

• (y^2/20) - (x^2/5) = 1

• (y^2/10) - (x^2/15) = 1

• (y^2/25) + (x^2/25) = 1

• (y^2/25) - (x^2/0) = 1

A soccer field is designed in the shape of an ellipse. If the distance between the foci is 10 meters and the length of the major axis is 30 meters, what is the equation of the ellipse?

• (x^2/225) + (y^2/200) = 1

• (x^2/400) + (y^2/100) = 1

• (x^2/225) + (y^2/150) = 1

• (x^2/100) + (y^2/300) = 1

A fountain is designed in the shape of a parabola. If the vertex is at the origin and the focus is at (0, 4), what is the equation of the parabola?

• y = -4x^2

• y = (1/4)x^2

• y = (1/8)x^2

• y = (1/16)x^2

A circular track has a radius of 50 meters. What is the equation of the circle that represents the track?

• x² + y² = 2000

• x² + y² = 1000

• x² + y² = 2500

• x² + y² = 3000

A bridge is designed with an arch that is a segment of a parabola. If the arch reaches a maximum height of 15 meters at its vertex and spans 30 meters at the base, what is the equation of the parabola?

• y = 1/15(x - 15)² + 15

• y = -1/15(x - 15)² + 15

• y = -1/30(x - 15)² + 15

• y = -1/15(x)² + 15