JEE Mains · Maths · STD 11 - 9. straight line
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 \(\triangle OAB\) is \(\frac{98}{3} \sqrt{3}\), then \(a ^2- b ^2\) is equal to:
- A \(\frac{392}{3}\)
- B \(196\)
- C \(\frac{196}{3}\)
- D \(98\)
Answer & Solution
Correct Answer
(A) \(\frac{392}{3}\)
Step-by-step Solution
Detailed explanation
Equation of straight line : \(\frac{ x }{ a }+\frac{ y }{ b }=1\) Or \(x \cos \frac{\pi}{3}+y \sin \frac{\pi}{3}=p\) \(\frac{x}{2}+\frac{y \sqrt{3}}{2}=p\) \(\frac{x}{3 p}+\frac{y}{2 p}=1\) Comparing both \(: a =2 p , b =\frac{2 p }{\sqrt{3}}\) Now area of…
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