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JEE Main & Advanced Mathematics Straight Line Question Bank Slope of line, Equation of line in different forms

  • question_answer
    If a and b are two arbitrary constants, then the straight line \[(a-2b)x+(a+3b)y+3a+4b=0\]will pass through [RPET 1990]

    A)            \[(-1,\ -2)\]                                

    B)            (1, 2)

    C)            \[(-2,\ -3)\]                                

    D)            (2, 3)

    Correct Answer: A

    Solution :

               \[(a-2b)x+(a+3b)y+3a+4b=0\]                    or \[a\text{ }(x+y+3)+b\text{ }(-2x+3y+4)=0\], which represents a family of straight lines through point of intersection of \[x+y+3=0\]and \[-2x+3y+4=0\]i.e, (? 1, ? 2).          Trick: Point (-1, -2) satisfies the given equation of straight line.


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