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JEE Main 06-Apr-2024 Paper - Shift 1 — JEE STD 11 Science — Question

Gujarat BoardEnglish MediumSTD 11 ScienceJEEJEE Main 06-Apr-2024 Paper - Shift 14 Marks
MCQ
Let a variable line of slope $m > 0$ passing through the point $(4, –9)$ intersect the coordinate axes at the points $A$ and $B$. the minimum value of the sum of the distances of $A$ and $B$ from the origin is
  • A
    25
  • B
    30
  • C
    15
  • D
    10
✓

Answer

equation of line is
$y+9=m(x-4)$
$\therefore A=\left(\frac{9+4 m}{m}, 0\right)$
$ B=(0,-9-4 m)$
$\therefore OA+OB$
$=\frac{9+4 m}{m}+9+4 m$
$\because m >0$
$=13+\frac{9}{m}+4 m$
$\because \frac{4 m+\frac{9}{m}}{2} \geq \sqrt{36} $
$\Rightarrow 4 m+\frac{9}{m} \geq 12$
$\therefore OA + OB \geq 25$

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