Q6 of 71 Page 27

Find the equation of the hyperbola, referred to its principal axes as axes of coordinates, in the following cases:

conjugate axis is 5 and the distance between foci = 13

Given: the distance between the foci = 13 and conjugate axis is 5


To find: the equation of the hyperbola


Formula used:


For hyperbola:



Distance between the foci is 2ae and b2 = a2(e2 – 1)


Length of conjugate axis is 2b


Therefore




2ae = 13




b2 = a2(e2 – 1)


⇒ b2 = a2e2 – a2





Equation of hyperbola is:







Hence, required equation of hyperbola is 25x2 – 144y2 = 900


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