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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Equations of circle, Geometrical problems regarding circle

  • question_answer
     For all values of \[\theta \], the locus of the point of intersection of the lines \[x\cos \theta +y\sin \theta =a\] and \[x\sin \theta -y\cos \theta =b\]  is

    A)            An ellipse                                 

    B)            A circle

    C)            A parabola                               

    D)            A hyperbola

    Correct Answer: D

    Solution :

               The point of intersection is                    \[x=a\cos \theta +b\sin \theta \]                    \[y=a\sin \theta -b\cos \theta \].                    Therefore, \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}+{{b}^{2}}\].                    Obviously, it is equation of a circle.


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