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

  • question_answer
    If \[{{p}_{1}},{{p}_{2}}\] are the lengths of the normal drawn from the origin on the lines\[x\cos \theta +ysin\theta =2acos4\theta \] And \[x\sec \theta +y\cos ec\theta =4a\cos 2\theta \] respectively, and \[m{{p}^{2}}_{1}+n{{p}^{2}}_{2}=4{{a}^{2}}.\] Then

    A) \[m=1,n=1\]

    B) \[m=1,n=4\]

    C) \[m=4,n=1\]

    D) \[m=1,n=-1\]

    Correct Answer: B

    Solution :

    [b] \[{{p}^{2}}_{1}=4{{a}^{2}}{{\cos }^{2}}4\theta \] \[{{p}^{2}}_{2}=\frac{16{{a}^{2}}{{\cos }^{2}}2\theta }{{{\sec }^{2}}\theta +\cos e{{c}^{2}}\theta }=16{{a}^{2}}{{\cos }^{2}}2\theta {{\cos }^{2}}\theta {{\sin }^{2}}\theta \]\[={{a}^{2}}{{\sin }^{2}}4\theta \] \[\therefore {{p}^{2}}_{1}+4{{p}^{2}}_{2}=4{{a}^{2}}\]


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