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

  • question_answer
    A vertex of equilateral triangle is (2, 3) and equation of opposite side is \[x+y=2,\] then the equation of one side from rest two, is [IIT 1975]

    A)            \[y-3=2(x-2)\]                          

    B)            \[y-3=(2-\sqrt{3})(x-2)\]

    C)            \[y-3=(\sqrt{3}-1)(x-2)\]        

    D)            None of these

    Correct Answer: B

    Solution :

               \[y-3=\tan (\theta \pm {{60}^{o}})(x-2)\]                    As \[\theta ={{135}^{o}},\]So \[y-3=\frac{-1\pm \sqrt{3}}{1\mp (-\sqrt{3})}(x-2)\]                    i.e., \[y-3=\frac{-1+\sqrt{3}}{\sqrt{3}+1}(x-2)=(2-\sqrt{3})(x-2)\].


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