2. Questions Bank
  3. JEE Main & Advanced
  4. Mathematics
  5. Circle and System of Circles

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

  • question_answer
    A tangent to the circle \[{{x}^{2}}+{{y}^{2}}=5\]at the point (1,?2)..... the circle \[{{x}^{2}}+{{y}^{2}}-8x+6y+20=0\]                    [IIT 1975]

    A)            Touches                                   

    B)            Cuts at real points

    C)            Cuts at imaginary points         

    D)            None of these

    Correct Answer: A

    Solution :

               Tangent is \[x-2y-5=0\] and points of intersection with circle \[{{x}^{2}}+{{y}^{2}}-8x+6y+20=0\] are given by                    \[4{{y}^{2}}+25+20y+{{y}^{2}}-16y-40+6y-20=0\]                    \[\Rightarrow 5{{y}^{2}}+10y+5=0\]                    \[\Rightarrow y=-1\]and \[x=-3\] i.e., touches.


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