Question

If the angle between the lines represented by the equation $y^2+hxy-x^{2}ta{n}^{2}A=0$ be 2A, then k=

• A. 0
• B. 1
• C. 2
• D. tan A

Answer 1

The correct option is A

0

$\tan \theta =\frac{2\sqrt{h^2-ab}}{a+b}$
Here tan2A = $\frac{2\sqrt{\frac{k^2}{4}+ta{n}^{2}A}}{1-ta{n}^{2}A}$

$\Rightarrow \frac{2tanA}{1-ta{n}^{2}A}=\frac{2\sqrt{\frac{k^2}{4}+ta{n}^{2}A}}{1-ta{n}^{2}A}$

$\Rightarrow \frac{k^2}{4}+ta{n}^{2}A=ta{n}^{2}A\Rightarrow k=0$