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KVPY2011MathematicsQuadratic Equation

Let a, b, x, y be real numbers such that a²+b²=81, x²+y²=121 and a x+b y=99 . Then the set of all possible values of ay - bx is -

Options

  1. A(0, 9 11 ]
  2. B(0, 9 11 )
  3. C0
  4. D[ 9 11 , )

Correct answer

C. 0

Step-by-step solution

a²+b²=81x²+y²=121a x+b y=99 (a²+b² ) (x²+y² )=(81)(121) ...(1) and (a x+b y)²=(99)² ...(2) (1)-(2) (ay -b x)²=0 ay -b x=0

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