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JEE Main & Advanced Sample Paper JEE Main Sample Paper-30

  • question_answer
    The number of points (a, b), \[(a,b\in I)\] in the x-y plane from where two mutually perpendicular tangents can be drawn to the hyperbola\[\frac{{{x}^{2}}}{25}-\frac{{{y}^{2}}}{9}=1\], is

    A)  1                                            

    B)  2

    C)  4             

    D)  infinite

    Correct Answer: C

    Solution :

    Point (a, b) must lie on the director circle \[{{x}^{2}}+{{y}^{2}}=16\] \[\left( \frac{\sum\limits_{r=1}^{n}{8{{r}^{3}}}}{\sum\limits_{r=1}^{n}{27{{r}^{3}}}} \right)\,={{\left( \frac{8}{27} \right)}^{1/3}}\,=\frac{2}{3}\] Number of points (a, b) on the circle whose abscissa and ordinate both are integers are 4 i.e. (4, 0) (0, 4) (-4, 0) (0, -4).                          


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