Asymptotes of a hyperbola are represented by $2 x^{2} + 3 x y - 2 y^{2} + 2 x - y = 0.$ The eccentricity of hyperbola can be

\sqrt{\frac{3}{2}}

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\sqrt{\frac{5}{3}}

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\sqrt{2}

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indeterminate

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Solution

The correct option is D $\sqrt{2}$
Angle between asymptotes of a rectangular hyperbola are $90^{\circ}$
Since $a + b = 0$ , these asymptotes are asymptotes to a rectangular hyperbola.
And we know eccentricity of a rectangular hyperbola is $e = \sqrt{2}$
Hence, option 'C' is correct.

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