JEE Main & Advanced Mathematics Sets Question Bank Critical Thinking

  • question_answer
    If \[A=[(x,\,y):{{x}^{2}}+{{y}^{2}}=25]\] and B = \[[(x,\,y):{{x}^{2}}+9{{y}^{2}}=144]\], then \[A\cap B\] contains [AMU 1996; Pb. CET 2002]

    A) One point

    B) Three points

    C) Two points

    D) Four points

    Correct Answer: D

    Solution :

    A = Set of all values (x, y) : \[{{x}^{2}}+{{y}^{2}}=25={{5}^{2}}\] B = \[\frac{{{x}^{2}}}{144}+\frac{{{y}^{2}}}{16}=1\] i.e., \[\frac{{{x}^{2}}}{{{(12)}^{2}}}\] + \[\frac{{{y}^{2}}}{{{(4)}^{2}}}=1\]. Clearly, A Ç B consists of four points.

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