Question

A straight line cuts off the intercepts $OA = a$ and $OB = b$ on the positive directions of $x$-axis and $y$ axis respectively If the perpendicular from origin $O$ to this line makes an angle of $\frac{\pi}{6}$ with positive direction of $y$-axis and the area of $\triangle O A B$ is $\frac{98}{3} \sqrt{3}$, then $a^2-b^2$ is equal to :

• A. $\frac{392}{3}$
• B. $\frac{196}{3}$
• C. 196
• D. 98

Answer 1

Answer: (A)

$\frac{392}{3}$

Answer 2

Equation of straight line : ax​+by​=1
Or xcos3π​+ysin3π​=p
2x​+2y3​​=p
3px​+2py​=1
Comparing both : a=2p,b=3​2p​
Now area of △OAB=21​⋅ab=398​⋅3​
21​⋅2p⋅3​2p​=398​⋅3​
p2=49
a2−b2=4p2−34p2​=32​4p2
=38​⋅49=3392​