(D) The angle $\theta$ between the pair of lines $ax^2 + 2hxy + by^2 = 0$ is given by $\tan \theta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} \right|$.Gi

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(D) The angle $\theta$ between the pair of lines $ax^2 + 2hxy + by^2 = 0$ is given by $\tan \theta = \left| \frac{2\sqrt{h^2 - ab}}{a + b} \right|$.Given $a = 12$,$b = 7$,and $\tan \theta = \frac{8}{19}$.Substituting the values,we get $\frac{8}{19} = \left| \frac{2\sqrt{h^2 - 12 \times 7}}{12 + 7} \right|$.$\frac{8}{19} = \frac{2\sqrt{h^2 - 84}}{19}$.$8 = 2\sqrt{h^2 - 84}$.$4 = \sqrt{h^2 - 84}$.Squaring both sides,$16 = h^2 - 84$.$h^2 = 100$.$h = \pm 10$.

Class 11 Mathematics Pair of straight lines Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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If $\theta$ is the acute angle between the pair of lines $12x^2 + 2hxy + 7y^2 = 0$ and $\tan \theta = \frac{8}{19}$,then $h =$

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$\pm 6$
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$\pm 7$
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$\pm 8$
D
$\pm 10$

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Pair of straight lines

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Angle between the pair of straight lines, Condition for parallel and perpendicular lines

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