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Q)

Angle between the asymptotes of the hyperbola $3x^2+7xy+2y^2-11x-7y+10=0$ is

$\begin{array}{1 1}(A)\;45^{\circ} \\(B)\;105^{\circ} \\(C)\;60^{\circ} \\(D)\;\text{none of these} \end{array}$

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A)
Equation of the hyperbola is
$3x^2+7xy+2y^2-11x-7y+10=0$ ----(1)
Equation of the asymptotes is
$3x^2+7xy+2y^2-11x-7y+c=0$-----(2)
So that (2) represent pair of straight line.
$\therefore $ Angle between the asymptotes is
$\tan^{-1} \bigg(2 \sqrt {\large\frac{{49}{4}-6}{5}}\bigg)$$=\tan ^{-1}$
$\qquad=\large\frac{\pi}{4} $$=45^{\circ}$
Hence A is the correct.
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