Find the equation of the hyperbola centered at the origin with a focus at (5,0) and a transverse axis of length 6.

Answer 1

Standard form of hyperbola with foci on the x axis x^2/a^2 - y^2/b^2 = 1

a = half of length of transverse axis = 6/2 = 3

To find b, solve c^2 = a^2 + b^2

c = distance from center to focus = 5

25 = 9 + b^2

b = 4

Equation of hyperbola is x^2/9 + y^2/16 = 1

Answer 2

Equation of hyperbola x²/a² - y²/b² = 1. By condition we have c = 5, 2b = 6, b = 3. Then a² = c² - b², a² = 25 - 9 = 16. So, equation of hyperbola: x²/16 - y²/9 = 1;

Answer 3

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