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MHT CET20244 May 2024Evening ShiftMathematicsStraight LinesActual

If O (0,0), A (1,2) and B (3,4) are the vertices of triangle OAB , then the joint equation of the altitude and median drawn from O is

Options

  1. A3 x^2-x y-2 y^2=0
  2. B3 x^2+x y+2 y^2=0
  3. C3 x^2-x y+2 y^2=0
  4. D3 x^2+x y-2 y^2=0

Correct answer

D. 3 x^2+x y-2 y^2=0

Step-by-step solution

OD is the median aligned & D ( 1+3 2 , 2+4 2 ) & D (2,3) aligned Equation of OD is y=m x aligned & y= 3 2 x & 3 x-2 y=0 aligned Slope of line A B= 2 2 =1 Given, OE AB Slope of OE =-1 Equation of OE is y=m x aligned & y=-x & x+y=0 aligned Joint equation of median and altitude is aligned & (3 x-2 y)(x+y)=0 & 3 x^2+x y-2 y^2=0 aligned

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