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COMEDK2024Morning ShiftMathematicsApplication of DerivativesActual

The point on the curve x^2=x y which is closest to (0,5) is

Options

  1. A(- 5 2 , 5 2 )
  2. B( 5 2 , 5 2 )
  3. C(0, 5)
  4. D(0, 2)

Correct answer

C. (0, 5)

Step-by-step solution

The curve x^2 = xy can be rewritten as x(x-y) = 0 , giving two lines: x = 0 (y-axis) and y = x . Checking if (0,5) lies on the curve: substituting x = 0 gives 0 = 0 , which is satisfied. So (0,5) already lies on the curve (on the x = 0 branch), and the distance is exactly 0. The closest point is (0, 5) itself.

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