JAMIA MILLIA ISLAMIA Jamia Millia Islamia Solved Paper-2004

  • question_answer
        The angle between the lines \[\frac{{{x}^{2}}}{64}+\frac{{{y}^{2}}}{100}=1\]and \[{{y}^{2}}=4x\] is equal to :

    A)  \[(-1,0)\]                            

    B)  \[\left( 0,1 \right)\]

    C)  \[\left( 0,-\text{l} \right)\]                         

    D)  \[{{x}^{2}}-4x-4y+4=0\]

    Correct Answer: A

    Solution :

                    \[\theta ={{\cos }^{-1}}\left[ \frac{3+0-5}{\sqrt{1+1}\sqrt{9+16+25}} \right]\]\[={{\cos }^{-1}}\left( \frac{-2}{10} \right)\] \[\left[ \because \cos \theta =\frac{a{{a}_{1}}+b{{b}_{1}}+c{{c}_{1}}}{\sqrt{{{a}^{2}}+{{b}^{2}}{{c}^{2}}}\sqrt{a_{1}^{2}+b_{1}^{2}+c_{1}^{2}}} \right]\]\[={{\cos }^{-1}}\left( \frac{1}{5} \right)\]


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