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Question
The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is ______.
Options
`4/49 x^2 - 196/51 y^2` = 1
`49/4 x^2 - 51/196 y^2` = 1
`4/49 x^2 - 51/196 y^2` = 1
None of these
Solution
The length of the transverse axis along x-axis with centre at origin of a hyperbola is 7 and it passes through the point (5, –2). The equation of the hyperbola is `4/49 x^2 - 51/196 y^2` = 1.
Explanation:
Let `x^2/a^2 - y^2/b^2` = 1 represent the hyperbola.
Then according to the given condition
The length of the transverse axis
i.e., 2a = 7
⇒ a = `7/2`.Also, the point (5, –2) lies on the hyperbola
So, we have `4/49 (25) - 4/b^2` = 1
Which gives `b^2 = 196/51`.
Hence, the equation of the hyperbola is `4/49 x^2 - 51/196 y^2` = 1.
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