Question

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

• A. $0$
• B. $2$
• C. $4$
• D. $-2$

Answer 1

The correct option is A $0$

$\tan 2A=\frac{2\sqrt{\frac{K^2}{4}+{\tan }^{2}A}}{1-{\tan }^{2}A}$

$\frac{2\tan A}{\left(1-{\tan }^{2}A\right)}=\frac{2\sqrt{\frac{K^2}{4}+{\tan }^{2}A}}{1-{\tan }^{2}A}$

${\tan }^{2}A=\frac{K^2}{4}+{\tan }^{2}A$

$=K=0$

Hence,

option $\left(A\right)$ is correct answer.