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Question

If the line lx + my = 1 be a tangent to the circle x2+y2=a2, then the locus of the point (l, m) is
  1. A straight line

  2. A parabola
  3. A Circle

  4. An ellipse


Solution

The correct option is C

A Circle


If the line lx + my - 1 = 0 touches the circle x2+y2=a2, then applying the condition of tangency, we have ±l.0+m.01l2+m2=a

On squaring and simplifying, we get the required locus x2+y2=1a2. Hence it is a circle.

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