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MHT CET20249 May 2024Evening ShiftMathematicsStraight LinesActual

A line 4 x+y=1 passes through the point A (2,-7) meets the line BC whose equation is 3 x-4 y+1=0 at the point B . The equation of the line A C so that A B=A C is

Options

  1. A52 x+89 y+519=0
  2. B52 x+89 y-727=0
  3. C52 x-89 y+519=0
  4. D52 x-89 y-727=0

Correct answer

A. 52 x+89 y+519=0

Step-by-step solution

Slopes of A B and B C are -4 and 3 4 respectively. Let be the angle between AB and BC . Then, = | -4- 3 4 1-4 ( 3 4 ) |= 19 8 ...(i) Since A B=A C ABC = ACB = the line A C also makes an angle with B C . If m is the slope of the line A C , then its equation is y+7= m (x-2) ...(ii) Now, = [ m - 3 4 1+ m 3 4 ] 19 8 = 4 ~m -3 4+3 ~m ...[From (i)] m =-4 or - 52 89 But slope of A B is -4 , so slope of AC is - 52 89 . Therefore, the equation of line AC given by (ii) is 52 x+89 y+519=0 .

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