Let m, n be real numbers such that 0 ≤ m ≤ √{3} and -√{3} ≤ n ≤ 0 . minimum possible are

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9.Straight Line

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Let $m, n$ be real numbers such that $0 \leq m \leq \sqrt{3}$ and $-\sqrt{3} \leq n \leq 0$. The minimum possible area of the region of the plane consisting of points $(x, y)$ satisfying in inequalities $y \geq 0, y-3 \leq m x$, $y -3 \leq nx$, is

A

$0$

B

$\frac{3 \sqrt{3}}{2}$

C

$3 \sqrt{3}$

D

$6 \sqrt{3}$

(KVPY-2021)

Solution

(c)

$y = mx +3$,$m \in[0, \sqrt{3}]$

$y = nx +3$,$n \in[-\sqrt{3}, 0]$

min area $=$ are $(\Delta PAB )=\frac{1}{2} \times 2 \sqrt{3} \times 3=3 \sqrt{3}$

Standard 11

Mathematics

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