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 System of circles

  • question_answer
    A circle touches the x-axis and also touches the circle with centre at (0, 3) and radius 2. The locus of the centre of the circle is [AIEEE 2005]

    A)            A hyperbola                             

    B)            A parabola

    C)            An ellipse                                 

    D)            A circle

    Correct Answer: B

    Solution :

               Let centre \[\equiv (h,k);\]As \[{{C}_{1}}{{C}_{2}}={{r}_{1}}+{{r}_{2}}\], (Given)                    \[\Rightarrow \,\,\,\sqrt{{{(h-0)}^{2}}+{{(k-3)}^{2}}}=|k+2|\]                    Þ \[{{h}^{2}}=5(2k-1)\]                    Hence locus, \[{{x}^{2}}=5(2y-1)\] , which is parabola.


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