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 Equations of circle, Geometrical problems regarding circle

  • question_answer
    A variable circle passes through the fixed point (2,0) and touches the y-axis . Then the locus of its centre is [EAMCET 2002]

    A)            A circle                                      

    B)            An Ellipse

    C)            A hyperbola                             

    D)            A parabola

    Correct Answer: D

    Solution :

               Suppose the centre of circle be\[(h,k)\]. Since it touches the\[y\text{-axis}\], \[\therefore \]radius of circle = h                    Now \[{{(h-2)}^{2}}+{{k}^{2}}={{h}^{2}}\]\[\Rightarrow \]\[{{h}^{2}}+4-4h+{{k}^{2}}={{h}^{2}}\]                    \[\Rightarrow \] \[{{k}^{2}}=4h-4\]. Hence the locus of centre is \[{{y}^{2}}=4x-4\], which is a parabola.


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