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NEST2012MathematicsApplication of Derivatives

Let X , Y be points on the same side of a straight line in a plane. Suppose P is a point on such that XP + PY is the minimum. Then

Options

  1. AThe line joining P and the midpoint of XY is perpendicular to .
  2. BX P and YP are equally inclined to .
  3. CThe ellipse with X and Y as foci passing through P has as its tangent at P .
  4. DThe circumcircle of triangle X Y P has as its tangent at P .

Correct answer

C. The ellipse with X and Y as foci passing through P has as its tangent at P .

Step-by-step solution

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