Finding Foci and Equations of Hyperbolas in Real Life

A satellite dish is shaped like a hyperbola. If the distance between the foci of the dish is 10 meters, what is the distance from the center to each focus?

• 3 meters

• 5 meters

• 7 meters

• 10 meters

A hyperbola is defined by the equation (x^2/36) - (y^2/16) = 1. What are the coordinates of the foci of this hyperbola?

• (3sqrt(13), 0) and (-3sqrt(13), 0)

• (0, 4) and (0, -4)

• (6, 0) and (-6, 0)

• (2sqrt(13), 0) and (-2sqrt(13), 0)

A car is traveling along a road that follows a hyperbolic path. If the equation of the road is given by (y^2/25) - (x^2/9) = 1, find the foci of the hyperbola.

• (0, √34) and (0, -√34)

• (0, 10) and (0, -10)

• (0, 5) and (0, -5)

• (3, 0) and (-3, 0)

A bridge is designed in the shape of a hyperbola. If the vertices are located at (0, 5) and (0, -5), what is the equation of the hyperbola?

• (y^2/25) - (x^2/b^2) = 1

• (y^2/20) - (x^2/15) = 1

• (y^2/25) + (x^2/25) = 1

• (y^2/30) - (x^2/10) = 1

A hyperbola has foci at (0, 6) and (0, -6). If the distance between the vertices is 8, write the equation of the hyperbola in standard form.

• (y^2/8) - (x^2/32) = 1

• (y^2/10) - (x^2/25) = 1

• (y^2/16) - (x^2/20) = 1

• (y^2/20) - (x^2/16) = 1

A hyperbola is represented by the equation (x^2/49) - (y^2/25) = 1. Determine the coordinates of the foci of this hyperbola.

• (±5, ±12)

• (±√74, 0)

• (±10, 0)

• (±7, 0)

A scientist models the path of a comet using a hyperbola. If the equation of the hyperbola is (x^2/64) - (y^2/36) = 1, what are the foci of the comet's path?

• (6, 0) and (-6, 0)

• (8, 0) and (-8, 0)

• (10, 0) and (-10, 0)

• (12, 0) and (-12, 0)

A hyperbola has its center at the origin and its foci at (0, ±5). If the distance between the vertices is 6, find the equation of the hyperbola.

• (x^2/9) - (y^2/16) = 1

• (y^2/9) - (x^2/16) = 1

• (y^2/16) - (x^2/9) = 1

• (y^2/25) - (x^2/36) = 1

A hyperbola is defined by the equation (y^2/16) - (x^2/9) = 1. What are the coordinates of the foci?

• (0, 6) and (0, -6)

• (0, 5) and (0, -5)

• (3, 4) and (3, -4)

• (5, 0) and (-5, 0)

A hyperbola has foci at (±4, 0) and vertices at (±3, 0). Write the equation of the hyperbola in standard form.

• (x^2/16) - (y^2/5) = 1

• (x^2/9) + (y^2/7) = 1

• (x^2/9) - (y^2/7) = 1

• (x^2/12) - (y^2/3) = 1