Q111 / 160 · TS EAMCET 2022 (20 Jul Shift 2) · Mathematics

If $\theta$ is the angle between the curves $x^2-y^2=4$ and $y^2=3 x$ then $\tan \theta=$

A
$\frac{5}{3 \sqrt{3}}$
Correct answer
B
$\frac{5}{6 \sqrt{3}}$
C
$\frac{5}{18}$
D
$\frac{5}{6}$

Solution

Given curves are $x^2-y^2=4$ and $y^2=3 x$ on solving curves we get $\mathrm{x}=4$ and $\mathrm{y}=\sqrt{3}$ Now $\tan \theta=\left|\frac{\frac{4}{\sqrt{3}}-\frac{3}{2 \sqrt{3}}}{1+\frac{4}{\sqrt{3}} \times \frac{3}{2 \sqrt{3}}}\right|=\frac{5}{6 \sqrt{3}}$

Hence, the correct answer is option: 'B'.

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