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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.
`x^2/16 - y^2/9 = 1`
उत्तर
Equation of hyperbola `x^2/16 - y^2/9 = 1`
The transverse axis is along the x-axis.
a2 = 16, b2 = 9
∴ c2 = a2 + b2 = 16 + 9 = 25
∴ a = 4, b = 3, c = 5
The coordinates of the vertices are (± a, 0) or (± 4, 0)
The coordinates of the foci are (± c, 0) or (± 5, 0)
Eccentricity = e = `c/a = 5/4`
length of the latus rectum = `(2b^2)/a = (2 xx 9)/4 = 9/2`
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