Question

If the angle between two lines represented by $2x^2 + 5xy + 3y^2 + 7y + 4 = 0$ is $\tan^{-1} m$, then m is equal to

• A. $1/5$
• B. $1$
• C. $7/5$
• D. $7$

Hint:

For pair of lines, $\tan\theta = \frac{2\sqrt{h^2-ab}}{|a+b|}$.

Answer 1

The Correct Option is B

Step 1: For pair of lines $ax^2+2hxy+by^2=0$, $\tan\theta = \frac{2\sqrt{h^2-ab}}{a+b}$. Here $a=2$, $h=5/2$, $b=3$.}
Step 2: $\tan\theta = \frac{2\sqrt{(25/4)-6}}{5} = \frac{2\sqrt{1/4}}{5} = \frac{1}{5}$. So $m=1/5$. Option (A).}