11th Class Mathematics Sample Paper Mathematics Olympiad - Sample Paper-1

  • question_answer A and B are two fixed points. The locus of a point p such that \[\angle \mathbf{APB}\] is a right angle, is

    A) \[2{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]        

    B) \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]    

    C) \[{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]                        

    D) \[2{{x}^{2}}-{{y}^{2}}={{a}^{2}}\]

    Correct Answer: B

    Solution :

    [b] \[\because \]The fixed point A & B will be the extreme point on the diameter of a circle. P be any point on the circle. So, equation of the circle, whose radius is a and centre be the origin be \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\] Hence, option [b] is correct.

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