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If the eccentricity of hyperbola x^2/a^2...

If the eccentricity of hyperbola `x^2/a^2-y^2/b^2=1` is `5/4` and `2x+3y-6=0` is a focal chord of hyperbola, then length of transverse axis is:

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Eccentricity of hyperbola `,e = 5/4`
Focii of a hyperbola is `(+-ae,0)`.
Now, `2x+3y-6 = 0` is the focal chord of hyperbola.
`:. 2(+-ae)+3(0) - 6 = 0`
`=>2(+-5/4a) = 6`
`=>+-5/2a = 6`
`=> a = +-12/5`
`=>|a| = 12/5`
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