Question

The center of a hyperbola is located at the origin. One focus is located at (0, 20), and its associated directrix is represented by the line y = -256/20. What is the equation of the hyperbola?

Answer 1

To find the equation of the hyperbola, we need to determine the coordinates of the other focus and the eccentricity of the hyperbola.

Step-by-step explanation:

To find the equation of the hyperbola, we need to determine the coordinates of the other focus and the eccentricity of the hyperbola. Since we already have the coordinates of one focus (0, 20) and the equation of the directrix (y = -256/20), we can find the distance between the focus and directrix, which represents the eccentricity.

The distance between the focus and the directrix is given by the formula: d = |p/e|, where p is the distance between the center and focus, and e is the eccentricity.

Using the known coordinates of the focus and the equation of the directrix, we can solve for the eccentricity and obtain the equation of the hyperbola.

Answer 2

D)
`y^(2)/16^(2) - x^(2) /12^(2) =1`

Step-by-step explanation:

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