Q86 / 160 · AP EAMCET 2023 (17 May Shift 1) · Mathematics

The absolute value of the tangent of the difference of the angles made by the lines $4 x^2-24 x y+11 y^2=0$ with the $\mathrm{X}$-axis is

  • A
    $\frac{4}{11}$
  • B
    $\frac{24}{11}$
  • Correct answer
    C
    $\frac{4}{3}$
  • D
    $\frac{11}{24}$

Solution

$\because 4 x^2-24 x y+11 y^2=0 \Rightarrow(2 x-y)(2 x-11 y)=0$ $\therefore$ Pair of equation of lines are $2 x-y=0 \& 2 x-11 y=0$ and their angles from $x$-axis is: $\begin{aligned} & \theta_1=\tan ^{-1} 2 \& \theta_2=\tan ^{-1} \frac{2}{11} \\ & \text { Now, } \tan \left|\theta_1-\theta_2\right| \\ & =\tan \left|\tan ^{-1} 2-\tan ^{-1} \frac{2}{11}\right|=\tan \left|\tan ^{-1} \frac{2-\frac{2}{11}}{1+\frac{4}{11}}\right| \\ & =\tan \left(\tan ^{-1} \frac{4}{3}\right)=\frac{4}{3} \end{aligned}$

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

Relevant Questions