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JEE Main & Advanced Mathematics Circle and System of Circles Question Bank Tangent and normal to a circle

  • question_answer
    The equations of the tangents to circle \[5{{x}^{2}}+5{{y}^{2}}=1\], parallel to line \[3x+4y=1\] are                           [J & K 2005]

    A)            \[3x+4y=\pm 2\sqrt{5}\]      

    B)            \[6x+8y=\pm \sqrt{5}\]

    C)          \[3x+4y=\pm \sqrt{5}\]     

    D)            None of these

    Correct Answer: C

    Solution :

               Equation of tangent \[y=\frac{-3}{4}x\pm \frac{1}{\sqrt{5}}\sqrt{1+{{\left( \frac{-3}{4} \right)}^{2}}}\]                    Þ \[y=\frac{-3}{4}x\pm \frac{1}{\sqrt{5}}\sqrt{\frac{16+9}{16}}\]                    Þ \[4y=-3x\pm \sqrt{5}\Rightarrow 3x+4y=\pm \sqrt{5}\]


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