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Question
Find the equation of the hyperbola satisfying the given conditions:
Vertices (±7, 0), e = `4/3`
Solution
Vertices (+7, 0), e = `4/3`
Here, the vertices are on the x-axis.
Therefore, the equation of the hyperbola is of the form `x^2/a^2 - y^2/b^2 = 1`.
Since the vertices are (+7, 0), a = 7.
It is given that = `e = 4/3`
∴ `c/a = 4/3` `[e = c/a]`
= `c/7 = 4/3`
= `c = 28/3`
We know that a2 + b2 + c2
∴ 72 + b2 = `(28/3)^2`
= b2 = `784/9 - 49`
= b2 = `(784 - 441)/9 = (343)/9`
Thus, the equation of the hyperbala is `x^2/49 - (9y^2)/343 = 1`.
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