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Question
Find the equation of the hyperbola in the cases given below:
Foci (± 2, 0), Eccentricity = `3/2`
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Solution
e = `3/2`
Foci (±c ,0) = (±2, 0)
c = 2
ae = 2
`a(3/2)` = 2
a = `4/3`, a2 = `16/9`
b2 = c2 – a2
= `4 - 16/9`
= `20/9`
Equation of hyperbola
`x^2/"a"^2 - y^2/"b"^2` = 1
`x^2/(16/9) - y^2/(20/9)` = 1
`(9x^2)/16 - (9y^2)/20` = 1
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