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JEE Main & Advanced Mathematics Straight Line Question Bank Self Evaluation Test - Straight Lines & Pair Striaght Lines

  • question_answer
    The equation of the straight line which passes through the point \[(-4,3)\] such that the portion of the line between the axes is divided internally by the point in the ration 5 : 3 is

    A) \[9x-20y+96=0\]

    B) \[9x+20y=24\]

    C) \[20x+9y+53=0\]

    D) None of these

    Correct Answer: A

    Solution :

    [a] Let the line cuts the axes at points \[A(a,0)\] and\[B(0,b)\]. Now, given that \[(-4,3)\] divides AB in the ratio 5 : 3. Then, \[-4=3a/8\] and \[3=5b/8\]. Therefore \[a=-32/3\] and \[b=24/5.\] Then using the intercept form \[x/a+y/b=1,\] the equation of line is \[-\frac{3x}{32}+\frac{5y}{24}=1\] or \[9x-20y+96=0\]


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