The eccentricity the hyperbola `x=a/2(t+1/t), y=a/2(t-1/t)` is a.`sqrt(2)` . b. `sqrt(3)` c. `2sqrt(3)` d. `3sqrt(2)`

Explanation

`frac{4 x^{2}}{a^{2}}=t^{2}+frac{1}{t^{2}}+2 `

`Rightarrow frac{4 x^{2}}{a^{2}}-2=t^{2}+frac{1}{t^{2}} ldots(1) `

` frac{4 y^{2}}{a^{2}}=t^{2}+frac{1}{t^{2}}-2 `

`Rightarrow frac{4 y^{2}}{a^{2}}+2=t^{2}+frac{1}{t^{2}} ldots(2)`

From (1) and (2), we get:
`frac{4 x^{2}}{a^{2}}-frac{4 y^{2}}{a^{2}}=4 `

`Rightarrow frac{x^{2}}{a^{2}}-frac{y^{2}}{a^{2}}=1`

standard equation of hyperbola `a^{2}=b^{2}`.

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