A camera is placed in front of a hyperbolic mirror. The equation of the hyperbola that models the mirror is , where x and y are in inches. The camera is pointed toward the vertex of the hyperbolic mirror and is positioned such that the lens is at the nearest focus to that vertex.

Answer:

The lens is 1 inch from the mirror

Step-by-step explanation:

* Lets revise the equation of the hyperbola with center (0 , 0) and

 transverse axis parallel to the y-axis is y²/a² - x²/b² = 1

- The coordinates of the vertices are  (0 , ± a)

- The coordinates of the co-vertices are (± b , 0)  

- The coordinates of the foci are (0 , ± c) where c² = a² + b²

* Lets solve the problem

∵ The equation of the hyperbola is y²/16 - x²/9 = 1

∵ The form of the equation is y²/a² - x²/b² = 1

∴ a² = 16

∴ a = √16 = 4

∵ The coordinates of the vertices are  (0 , ± a)

∴ The coordinates of the vertices are  (0 , 4) , (0 , -4)

∴ b² = 9

∴ b = √9 = 3

∵ c² = a² + b²

∴ c² = 16 + 9 = 25

∴ c = √25 = 5

∵ The coordinates of the foci are (0 , ± c)

∴ The coordinates of the foci are (0 , 5) , (0 , -5)

∵ The camera is pointed towards the vertex of the hyperbolic mirror

   which is (0 , 4) and is positioned such that the lens is at the nearest

  focus to that vertex which is (0 , 5)

∴ The distance between the lens and the mirror equal the distance

   between the vertex and the focus

∵ The vertex is (0 , 4) and the nearest focus is (0 , 5)

∴ The distance = 5 - 4 = 1 inch

* The lens is 1 inch from the mirror

Answer:

1

Step-by-step explanation:

I answered this in edmentum and got this correct