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Question
Find the coordinates of the foci and the vertices, the eccentricity, and the length of the latus rectum of the hyperbola.
49y2 – 16x2 = 784
Solution
Equation of hyperbola: 49y2 – 16x2 = 784
Dividing by 784, `y^2/16 - x^2/49 = 1`
The transverse axis is along the y-axis.
a2 = 16, b2 = 49
∴ c2 = a2 + b2 = 16 + 49 = 65
∴ a = 4, b = 7, c = `sqrt65`
The coordinates of the vertices are (0, ± a) or (0, ± 4)
The coordinates of the foci are (0, ±c) or `(0, ±sqrt65)`
Eccentricity e = `c/a = sqrt65/4`
Length of the latus rectum = `(2b^2)/a`
= `(2 xx 49)/4`
= `49/2`
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