$3x+4y=2$ and $3y-4x-5=0$

The eccentricity of hyperbola whose asymptotes areis

The answer is 1.414.

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Clearly the given lines are perpendicular to each other because product of their slopes is equal to -1.

Now, we know that a conic (particularly hyperbola) whose asymptotes are perpendicular is a RECTANGULAR HYPERBOLA.

BASIC DEFINITION: A hyperbola whose both the major & minor axes are equal is called a RECTANGULAR HYPERBOLA.

We know, e= $\sqrt{ \frac{b^{2}}{a^{2}} +1}$ where e, a & b are respectively the eccentricity and half the major & minor axes.

Now for a rectangular hyperbola, a=b

Therefore $\boxed{e=\sqrt{2}}$