Question

If the acute angles between the pairs of lines $3x^2-7xy+4y^2=0$ and $6x^2-5xy+y^2=0$ be ${\theta }_1$ and ${\theta }_2$ respectively, then

• A. ${\theta }_1$ = ${\theta }_2$
• B. ${\theta }_1$ = 2${\theta }_2$
• C. $2{\theta }_1$ = ${\theta }_2$
• D. ${\theta }_1$ = 5${\theta }_2$

Answer 1

The correct option is A

${\theta }_1$ = ${\theta }_2$

$\tan \theta =\frac{2\sqrt{h^2-ab}}{a+b}$
$\text{Obviously}{\theta }_1=ta{n}^{-1}\left(\frac{2\sqrt{\frac{49}{4}-12}}{3+4}\right)=ta{n}^{-1}\left(\frac{1}{7}\right){\theta }_2=ta{n}^{-1}\left(\frac{2\sqrt{\frac{25}{4}-6}}{6+1}\right)=ta{n}^{-1}\left(\frac{1}{7}\right)$