JEE Main20257 Apr 2025Evening ShiftMathematicsStraight LinesActual

If the orthocentre of the triangle formed by the lines y=x+1, y=4 x-8 and y=m x+c is at (3,-1) , then m - c is :

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Correct answer

A. 0

Step-by-step solution

Solve line PQ & QR Point Q ( 1- c m -1 , 1- c m -1 +1 ) m_ 2 H = 1-c m-1 +2 1-c m-1 -3 = 1-c+2 m-2 1-c-3 m+3 =- 1 4 m _ 2 H = 1- c m -1 +2 1- c m -1 -3 = 1- c +2 ~m -2 1- c -3 ~m +3 =- 1 4 ...(1) m _ PH = 5 0 Slope of line QR (m) =0 Put value of m in equation (1) 1-c-2 1-c+3 =- 1 4 c=0 so m - c =0 Ans.

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