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Question
Find the equation of the hyperbola in the cases given below:
Centre (2, 1), one of the foci (8, 1) and corresponding directrix x = 4
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Solution
Distance CS = ae = 6 .......(1)
Directrix `"a"/x` = 4 .......(2)
(1) × (2)
⇒ ae × `"a"/"e"` = 24
a2 = 24
∴ c = ae = 6
b2 = c2 – a2
= 36 – 24 = 12
The transverse axis is parallel to x-axis
∴ `(x - "h")^2/"a"^2 - (y - "k")^2/"b"^2` = 1(h, k) = (2, 1)
`(x - 2)^2/24 - (y - 1)^2/12` = 1
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