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ISI2014-DCG-27

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Let $y^2-4ax+4a=0$ and $x^2+y^2-2(1+a)x+1+2a-3a^2=0$ be two curves. State which one of the following statements is true.

  1. These two curves intersect at two points
  2. These two curves are tangent to each other
  3. These two curves intersect orthogonally at one point
  4. These two curves do not intersect
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