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 = . what is the equation of the hyperbola? = 1 = 1 = 1 = 1

Answer 1

The equation of the hyperbola is D. $y^2/16^2-x^2/12^2=1$

Calculations and Parameters:

Given that the focus is at (0, 20)

Directrix is y=  -256/20

What is the relation between a, b, and c?

$a^2 +b^2 = c^2\\b^2 + (16)^2= (20)^2\\b^2= 400 -256\\b^2= 144$

b= 12

Making use of the vertices, foci, asymptotes, directrices, and standard equation, we find the equation of the hyperbola is $y^2/16^2-x^2/12^2=1$

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Answer 2

Answer:

D

Step-by-step explanation: