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COMEDK20269 May 2026Morning ShiftMathematicsStraight LinesActual

If a straight line passing through a fixed point (a, b) , where a, b > 0 , makes positive intercepts OA and OB on the coordinate axes, then the least value of OA + OB is:

Options

  1. A( a + b )^2
  2. Ba + b
  3. C( a + b )^3
  4. D( a - b )^2

Correct answer

A. ( a + b )^2

Step-by-step solution

Let the intercepts on the coordinate axes be and . The equation of the line is x + y = 1 . Since the line passes through (a, b) , we have a + b = 1 . We need to find the minimum value of OA + OB = + . Using the Cauchy-Schwarz inequality: ( + ) ( a + b ) ( a + b )^2 ( + ) (1) ( a + b )^2 Thus, the least value of OA + OB is ( a + b )^2 . Answer: ( a + b )^2

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