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JEE Main2007MathematicsCircleActual

Consider a family of circles which are passing through the point (-1,1) and are tangent to x- axis. If (h, k) are the co-ordinates of the centre of the circles, then the set of values of k is given by the interval

Options

  1. A0 < k < 1 / 2
  2. Bk 1 / 2
  3. C-1 / 2 k 1 / 2
  4. Dk 1 / 2

Correct answer

B. k 1 / 2

Step-by-step solution

Equation of circle (x-h)^2+(y-k)^2=k^2 It is passing through (-1,1) then aligned & (-1-h)^2+(1-k)^2=k^2 & h^2+2 h-2 k+2=0 & D 0 & 2 k-1 0 k 1 / 2. aligned

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