Applications of Derivatives
Optimization — Triangle Area
nta_pyq_2024_apr
Grade 12
Question:
A variable line $L$ passes through the point $(3,5)$ and intersects the positive coordinate axes at the points $A$ and $B$. The minimum area of the triangle $OAB$, where $O$ is the origin, is:
Step-by-Step Solution
Key Concept: Area $=\frac{5}{2}\cdot\frac{a^2}{a-3}\geq30$ by AM-GM.
Min area $=30$.
Correct Answer: 1