Q86 / 150 · MHT CET 2009 · Mathematics

If $\varphi^{\prime}$ is the angle between the lines $a x^{2}+2 h x y+b y^{2}=0$, then angle between $x^{2}+2 x y \sec \theta+y^{2}=0$ is

  • Correct answer
    A
    $\bar{\theta}$
  • B
    $2 \theta$
  • C
    $\frac{\theta}{2}$
  • D
    $3 \theta$

Solution

Angle between the lines $a x^{2}+2 h x y+b y^{2}=0$ is $\tan \theta=\left|\frac{2 \sqrt{h^{2}-a b}}{a+b}\right|$ For $x^{2}+2 x y \sec \theta+y^{2}=0$ $\begin{aligned} h &=\sec \theta, a=b=1 \\ \therefore \quad \tan \phi &=\mid \frac{2 \sqrt{\sec ^{2} \theta-1}}{1+1} \end{aligned}$ $=\frac{2 \tan \theta}{2}=\tan \theta$ $\therefore$ Angle between $x^{2}+2 x y \sec \theta+y^{2}=0$ is $\theta$.

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

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