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 Chord of contact of tangent, Pole and Polar

  • question_answer
    The pole of the line \[2x+3y=4\]w.r.t circle \[{{x}^{2}}+{{y}^{2}}=64\] is  [RPET 1996]

    A)            (32, 48)                                    

    B)            (48, 32)

    C)            (- 32, 48)                                  

    D)            (48, -32)

    Correct Answer: A

    Solution :

                Let pole be\[({{x}_{1}},\ {{y}_{1}})\]. Then the equation of the polar is, \[x{{x}_{1}}+y{{y}_{1}}={{a}^{2}}\]                    \[\therefore \ x{{x}_{1}}+y{{y}_{1}}=64\]                                                          ?. (i)                    Since (i) and line \[2x+3y=4\] represent the same straight line.                    \[\Rightarrow \frac{{{x}_{1}}}{2}=\frac{{{y}_{1}}}{3}=\frac{-64}{-4}\Rightarrow {{x}_{1}}=32,\ {{y}_{1}}=48\]                    Trick: Pole\[\left( \frac{-l{{a}^{2}}}{n},\ \frac{-m{{a}^{2}}}{n} \right)\Rightarrow (32,\ 48)\].


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