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QJEEM25Ma6d04: JEE Main 2025 Mathematics - Class 11 JEEM25Ma6d04 Solution: Two equal sides of an isosceles triangle are along and . If is…

Two equal sides of an isosceles triangle are along −x+2y=4-x + 2y = 4 and x+y=4x + y = 4 . If mm is the slope of its third side, then the sum, of all possible distinct values of mm , is:

Multiple Choice Options

  • A −210-2\sqrt{10}
  • B 12
  • C -6
  • D 6

Step-by-Step Verified Solution

JEE Main 2025 (Online) 28th January Evening Shift Mathematics - Straight Lines and Pair of Straight Lines Question 6 English Explanation

amp;tan⁡θ=m−121+12⋅m=−1−m1−m=m+1m−1amp;2m−12+m=m+1m−1amp;2m2−3m+1=m2+3m+2\begin{aligned}& \tan \theta=\frac{m-\frac{1}{2}}{1+\frac{1}{2} \cdot m}=\frac{-1-m}{1-m}=\frac{m+1}{m-1} \\& \frac{2 m-1}{2+m}=\frac{m+1}{m-1} \\& 2 m^2-3 m+1=m^2+3 m+2\end{aligned}

amp;m2−6m−1=0amp; sum of root =6amp; sum is 6\begin{aligned}& m^2-6 m-1=0 \\& \text { sum of root }=6 \\& \text { sum is } 6\end{aligned}

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