JEE Mains · Maths · STD 11 - 9. straight line
A variable line \(\mathrm{L}\) passes through the point \((3,5)\) and intersects the positive coordinate axes at the points \(\mathrm{A}\) and \(\mathrm{B}\). The minimum area of the triangle \(\mathrm{OAB}\), where \(\mathrm{O}\) is the origin, is :
- A \(30\)
- B \(25\)
- C \(40\)
- D \(35\)
Answer & Solution
Correct Answer
(A) \(30\)
Step-by-step Solution
Detailed explanation
\( \frac{x}{a}+\frac{y}{b}=1 \) \( \frac{3}{a}+\frac{5}{b}=1 \Rightarrow b=\frac{5 a}{a-3}, a>3\) \(Image\) \(\mathrm{A}=\frac{1}{2} \mathrm{ab}=\frac{1}{2} \mathrm{a} \frac{5 \mathrm{a}}{(\mathrm{a}-3)}=\frac{5}{2} \cdot \frac{\mathrm{a}^2}{\mathrm{a}-3}\)…
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