Verified Solution • 2025–26 Session moderate

QJEEM24Ma2b94: JEE Main 2024 Mathematics - Class 11 JEEM24Ma2b94 Solution: Let a variable line of slope passing through the point…

Let a variable line of slope m>0 passing through the point (4,−9)(4,-9) intersect the coordinate axes at the points AA and BB . The minimum value of the sum of the distances of AA and BB from the origin is

Multiple Choice Options

  • A 30
  • B 15
  • C 10
  • D 25

Step-by-Step Verified Solution

JEE Main 2024 (Online) 6th April Morning Shift Mathematics - Straight Lines and Pair of Straight Lines Question 10 English Explanation

amp;L:(y+9)=m(x−4)amp;A:(4+9m,0)amp;B:(0,−9−4m)amp;OA+OB]min⁡amp;⇒Emin⁡=4+9m+9+4mamp;E=13+9m+4mamp;dEdM=0⇒−9m2+4=0⇒m=±32\begin{aligned}& L:(y+9)=m(x-4) \\& A:\left(4+\frac{9}{m}, 0\right) \\& B:(0,-9-4 m) \\& O A+O B]_{\min } \\& \Rightarrow E_{\min }=4+\frac{9}{m}+9+4 m \\& E=13+\frac{9}{m}+4 m \\& \frac{d E}{d M}=0 \Rightarrow-\frac{9}{m^2}+4=0 \Rightarrow m= \pm \frac{3}{2}\end{aligned}

amp;d2EdM2=18m3gt;0 for m=32amp;∴Emin⁡=4+6+9+6=25\begin{aligned}& \frac{d^2 E}{d M^2}=\frac{18}{m^3}>0 \text { for } \quad m=\frac{3}{2} \\& \therefore E_{\min }=4+6+9+6=25\end{aligned}

Related Learning Resources & Exam Preparation

JEE Main PYQ Question Bank
Browse year-wise authentic previous years' questions with solutions
Authentic CBT Mock Tests
Simulate official exam environment with live timer and percentile scoring