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प्रश्न
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.
16x2 – 9y2 = 576
उत्तर
Equation of hyperbola: 16x2 – 9y2 = 576
On dividing by 576,
`x^2/36 - y^2/64 = 1`
The transverse axis is along the x-axis.
a2 = 36, b2 = 64
∴ c2 = a2 + b2 = 36 + 64 = 100
∴ a = 6, b = 8, c = 10
The coordinates of the vertices are (±a, 0) or (±6, 0)
The coordinates of the foci are (±c, 0) or (±10, 0)
Eccentricity e = `c/a = 10/6 = 5/3`
Length of the latus rectum = `(2b^2)/a`
= `(2xx 64)/6`
= `64/3`
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