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JEE Main & Advanced Mathematics Straight Line Question Bank Problems related to triangle and quadrilateral Locus

  • question_answer
    Two lines are drawn through (3, 4), each of which makes angle of 45o with the line \[x-y=2\], then area of the triangle formed by these lines is                          [RPET 2000]

    A)            9     

    B)            9/2

    C)            2     

    D)            2/9

    Correct Answer: B

    Solution :

               The equation of lines are \[y-{{y}_{1}}=\frac{m\pm \tan \alpha }{1\mp m\tan \alpha }(x-{{x}_{1}})\]                    Þ \[y-4=\frac{1\pm \tan 45{}^\circ }{1\mp \tan 45{}^\circ }(x-{{x}_{1}})\]                    Þ \[y-4=\frac{1\pm 1}{1\mp 1}(x-3)\] Þ \[y=4\] or \[x=3\]                    Hence, the lines which make the triangle are \[x-y=2,\] \[x=3\] and \[y=4\]. The intersection points of these lines are \[(6,\,4),\,(3,\,1)\] and \[(3,\,4)\]                    \ \[\Delta =\frac{1}{2}[6(-3)+3(0)+3(3)]\] \[=\frac{9}{2}\].


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