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JEE Main 2007
Exam
JEE Main
Year
2007
Subject
Mathematics
Chapter
Circle

JEE Main 2007 · Mathematics · Circle

Consider a family of circles which are passing through the point...

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

Options

  1. A0<k<1/20 < \mathrm{k} < 1 / 2
  2. Bk≥1/2k \geq 1 / 2
  3. C−1/2≤k≤1/2-1 / 2 \leq k \leq 1 / 2
  4. Dk≤1/2k \leq 1 / 2

Correct answer

B. k≥1/2k \geq 1 / 2

Step-by-step solution

Equation of circle (x−h)2+(y−k)2=k2(x-h)^2+(y-k)^2=k^2 It is passing through (−1,1)(-1,1) then (−1−h)2+(1−k)2=k2h2+2h−2k+2=0D≥02k−1≥0⇒k≥1/2.\begin{aligned} & (-1-h)^2+(1-k)^2=k^2 \\ & h^2+2 h-2 k+2=0 \\ & D \geq 0 \\ & 2 k-1 \geq 0 \Rightarrow k \geq 1 / 2. \end{aligned}
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