JEE Main & Advanced JEE Main Paper (Held On 12 April 2014)

  • question_answer
    For the two circles \[{{x}^{2}}+{{y}^{2}}=16\] and \[{{x}^{2}}+{{y}^{2}}-2y=0,\]there is/are   [JEE Main Online Paper ( Held On 12 Apirl  2014 )

    A) one pair of common tangents

    B) two pair of common tangents

    C) three pair of common tangents

    D) no common tangent

    Correct Answer: D

    Solution :

    Let, \[{{x}^{2}}+{{y}^{2}}=16\]or\[{{x}^{2}}+{{y}^{2}}={{4}^{2}}\]radius of circle \[{{r}_{1}}=4,\]centre \[{{C}_{1}}(0,0)\]we have, \[{{x}^{2}}+{{y}^{2}}-2y=0\] \[\Rightarrow \] \[{{x}^{2}}+({{y}^{2}}-2y+1)-1=0\] or\[{{x}^{2}}+{{(y-1)}^{2}}={{1}^{2}}\] Radius 1, centre \[{{C}_{2}}(0,1)\] \[|{{C}_{1}}{{C}_{2}}|=1\] \[|{{r}_{1}}-{{r}_{2}}|=|4-1|=3\] \[|{{C}_{1}}{{C}_{2}}|<|{{r}_{2}}-{{r}_{1}}|\] no common tangents for these two circles.

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