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

  • question_answer
    Equation of the tangent to the circle \[{{x}^{2}}+{{y}^{2}}={{a}^{2}}\]which is perpendicular to the straight line \[y=mx+c\]is 

    A)            \[y=-\frac{x}{m}\pm a\sqrt{1+{{m}^{2}}}\]                      

    B)            \[x+my=\pm \text{ }a\text{ }\sqrt{1+{{m}^{2}}}\]

    C)            \[x+my=\pm a\sqrt{1+{{(1/m)}^{2}}}\]                             

    D)            \[x-my=\pm a\sqrt{1+{{m}^{2}}}\]

    Correct Answer: B

    Solution :

               Line perpendicular to \[y=mx+c\] is \[y=-\frac{1}{m}x+\lambda \] and \[m\lambda =\pm a\sqrt{1+{{m}^{2}}}\]                    Hence required tangent is \[my+x=\pm a\sqrt{1+{{m}^{2}}}\].


You need to login to perform this action.
You will be redirected in 3 sec spinner