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What is the equation of the hyperbola ha...

What is the equation of the hyperbola having latus rectum and eccentricity 8 and `3/sqrt(5)` respectively? (A) ` x^2/25-y^2/20=1 ` (B) ` x^2/40-y^2/20 =1` (C) ` x^2/40-y^2/30=1` (D) ` x^2/30-y^2/25 = 1`

Text Solution

Verified by Experts

Latus rectum of the hyperbola `=8`
`:. (2b^2)/a = 8 => b^2 = 4a->(1)`
Eccentricity of the hyperbola `= 3/sqrt5`
`:. c/a = 3/sqrt5=>c^2/a^2 = 9/5`
Also, we know, `c^2 = a^2+b^2`
`:. a^2+b^2 = 9/5a^2`
`=>a^2+4a = 9/5a^2`
`=>5a^2+20a -9a^2 = 0`
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