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KVPY2019MathematicsStraight Lines

Let S be a subset of the plane defined by S = x , y : | x | + 2 | y | = 1 . Then, the radius of the smallest circle with centre at the origin and having non-empty intersection with S is

Options

  1. A1 5
  2. B1 5
  3. C1 2
  4. D2 5

Correct answer

B. 1 5

Step-by-step solution

The radius of the smallest circle with centre at the origin and having non-empty intersection with S = x , y : | x | + 2 | y | = 1 is radius of inscribed circle of rhombus having sides represented by equation | x | + 2 | y | = 1 . r = | 0 + 2 0 - 1 | 1 + 4 = 1 5

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