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Question
Identify the type of conic and find centre, foci, vertices, and directrices of the following:
`x^2/25 - y^2/144` = 1
Solution
It is Hyperbola.
The transverse axis the x-axis.
a2 = 25, b2 = 144
a = 5, b = 12
c2 = a2 + b2
= 25 + 144
= 169
c = 13
ae = 13
5e = 13
e = `13/5`
(a) Centre (0, 0)
(b) Vertex (± a, 0) = (± 5, 0)
(c) Foci (± c, 0) = (± 13, 0)
(d) Equation of the directrix
x = `+- "a"/"e" = +- 5/(13/5) = +- 25/13`
x = `+- 25/13`
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