JEE Main & Advanced Mathematics Conic Sections Question Bank Self Evaluation Test - Conic Sections

  • question_answer
    If the centre of the circle passing through the origin is (3, 4), then the intercepts cut off by the circle on x-axis and y-axis respectively are

    A) 3 unit and 4 unit

    B) 6 unit and 4 unit

    C) 3 unit and 8 unit

    D) 6 unit and 8 unit

    Correct Answer: D

    Solution :

    [d] Equation of circle having radius r and centre (3, 4) is \[={{(x-3)}^{2}}+{{(y-4)}^{2}}={{r}^{2}}\] If it is passing through (0, 0) \[\therefore \,\,\,\,{{(0-3)}^{2}}+{{(0-4)}^{2}}={{r}^{2}}\] \[\Rightarrow {{r}^{2}}=25\] equation of circle is \[{{(x-3)}^{2}}+{{(y-4)}^{2}}=25\] Putting y=0 \[\therefore \]  x = 6 unit = interception x-axis intercept on y axis (Putting x = 0) is \[y=8\] unit


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