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JEE Main & Advanced Mathematics Pair of Straight Lines Question Bank Equation of lines joining the origin to the point of intersection of a curve and a line and Distance between the pair of lines

  • question_answer
    Distance between the lines represented by the equation \[{{x}^{2}}+2\sqrt{3}xy+3{{y}^{2}}-3x-3\sqrt{3}y-4=0\]is                    [Roorkee 1989]

    A)            5/2

    B)            5/4

    C)            5    

    D)            0

    Correct Answer: A

    Solution :

               First check for parallel lines                    i.e., \[\frac{a}{h}=\frac{h}{b}=\frac{g}{f}\Rightarrow \frac{1}{\sqrt{3}}=\frac{\sqrt{3}}{3}=\frac{-3/2}{-3\sqrt{3}/2}\]            which is true, hence line are parallel. Applying formula for distance between two parallel straight lines, the required distance is\[2\sqrt{\frac{{{g}^{2}}-ac}{a(a+b)}}=2\sqrt{\frac{\frac{9}{4}+4}{4}=}\frac{5}{2}\].


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