Identifying and Graphing Hyperbolas in Real Life

A satellite dish is shaped like a hyperbola. If the distance between the foci is 10 meters and the distance from the center to a vertex is 4 meters, what is the equation of the hyperbola?

• (y^2/20) - (x^2/5) = 1

• (y^2/12) - (x^2/16) = 1

• (y^2/25) - (x^2/4) = 1

• (y^2/16) - (x^2/9) = 1

A hyperbola is used to model the path of a spacecraft. If the transverse axis is 12 meters and the conjugate axis is 16 meters, what is the standard form of the hyperbola's equation?

• (x^2/24) - (y^2/64) = 1

• (x^2/36) + (y^2/64) = 1

• (x^2/36) - (y^2/64) = 1

• (x^2/48) - (y^2/36) = 1

A car's headlights create a hyperbolic pattern on the road. If the distance between the foci is 14 feet and the distance from the center to a vertex is 7 feet, how would you graph this hyperbola?

• Graph the hyperbola centered at (0,0) with vertices at (7,0) and (-7,0), and foci at (0,7) and (0,-7).

• Graph the hyperbola centered at (0,0) with vertices at (14,0) and (-14,0), and foci at (14,0) and (-14,0).

• Graph the hyperbola centered at (0,0) with vertices at (0,7) and (0,-7), and foci at (0,7) and (0,-7).

• Graph the hyperbola centered at (0,0) with vertices at (7,0) and (-7,0), and foci at (7,0) and (-7,0).

A hyperbola is formed by the intersection of a cone and a plane. If the equation of the hyperbola is (y^2/9) - (x^2/16) = 1, how would you graph this hyperbola?

• Graph the hyperbola centered at (0,0) with vertices at (0, ±2) and asymptotes with slopes ±(2/3).

• Graph the hyperbola centered at (0,0) with vertices at (±3, 0) and asymptotes with slopes ±(3/5).

• Graph the hyperbola centered at (0,0) with vertices at (0, ±3) and asymptotes with slopes ±(3/4).

• Graph the hyperbola centered at (0,0) with vertices at (±4, 0) and asymptotes with slopes ±(4/3).

A radio tower is located at one focus of a hyperbola. If the distance from the center to the vertex is 5 miles and the distance between the foci is 8 miles, what is the equation of the hyperbola?

• y^2/36 - x^2/16 = 1

• x^2/25 - y^2/9 = 1

• y^2/49 - x^2/25 = 1

• y^2/25 - x^2/9 = 1

A hyperbola can model the trajectory of a comet. If the foci are located at (0, ±5) and the distance from the center to a vertex is 3, what is the equation of the hyperbola?

• (y^2/16) - (x^2/9) = 1

• (y^2/25) - (x^2/4) = 1

• (x^2/9) - (y^2/16) = 1

• (y^2/9) - (x^2/16) = 1

A hyperbola is used in a design for a cooling tower. If the transverse axis is 20 meters and the conjugate axis is 12 meters, what is the equation of the hyperbola?

• (x^2/64) - (y^2/25) = 1

• (x^2/100) - (y^2/36) = 1

• (y^2/36) - (x^2/100) = 1

• (x^2/144) - (y^2/49) = 1

A hyperbola is used to describe the path of two trains approaching each other. If the distance between the foci is 18 miles and the distance from the center to a vertex is 9 miles, how would you graph this hyperbola?

• Graph a circle centered at (0,0) with a radius of 9 miles.

• Graph a parabola with a vertex at (0,9) and a focus at (0,18).

• Graph an ellipse with foci at (0,9) and (0,-9).

• Graph a hyperbola centered at (0,0) with vertices at (9,0) and (-9,0), and foci at (9,0) and (-9,0).

A hyperbola is represented by the equation (x^2/25) - (y^2/16) = 1. Identify the vertices and foci of this hyperbola and explain how to graph it accurately.

• Vertices: (6, 0) and (-6, 0); Foci: (√50, 0) and (-√50, 0)

• Vertices: (4, 0) and (-4, 0); Foci: (√30, 0) and (-√30, 0)

• Vertices: (5, 0) and (-5, 0); Foci: (√41, 0) and (-√41, 0).

• Vertices: (5, 5) and (-5, -5); Foci: (0, √41) and (0, -√41)