JEE MAIN - Mathematics (2025 - 28th January Evening Shift - No. 6)
Two equal sides of an isosceles triangle are along $ -x + 2y = 4 $ and $ x + y = 4 $. If $ m $ is the slope of its third side, then the sum, of all possible distinct values of $ m $, is:
$-2\sqrt{10}$
12
-6
6
Explanation
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$$\begin{aligned} & \tan \theta=\frac{m-\frac{1}{2}}{1+\frac{1}{2} \cdot m}=\frac{-1-m}{1-m}=\frac{m+1}{m-1} \\ & \frac{2 m-1}{2+m}=\frac{m+1}{m-1} \\ & 2 m^2-3 m+1=m^2+3 m+2 \end{aligned}$$
$$\begin{aligned} & m^2-6 m-1=0 \\ & \text { sum of root }=6 \\ & \text { sum is } 6 \end{aligned}$$
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