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BITSAT2010MathematicsCircleActual

The line (a x+b y=1 ) cuts ellipse (c x^2+d y^2=1 ) only once if

Options

  1. A( ca ^2+ db ^2=1 )
  2. B( c a ^2 + d b ^2 =1 )
  3. C( a ^2 c + b ^2 ~d =1 )
  4. D(a c^2+b d^2=1 )

Correct answer

C. ( a ^2 c + b ^2 ~d =1 )

Step-by-step solution

Clearly (a x+b y=1 ) i.e (y=- a b x+ 1 b ) is tangent to ( aligned & cx ^2+ dy ^2=1 x ^2 1 c + y ^2 1 d =1 & ( 1 b )^2= ( 1 c ) (- a b )^2+ ( 1 d ) & 1= a^2 c + b^2 d aligned )

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