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BITSAT2024MathematicsCircleActual

If p and q be the longest and the shortest distance respectively of the point (-7,2) from any point ( , ) on the curve whose equation is x^2+y^2-10 x-14 y-51=0 , then G.M. of p

Options

  1. A2 11
  2. B5 5
  3. C13
  4. D11

Correct answer

A. 2 11

Step-by-step solution

The centre C of the circle =(5,7) and the radius = 5^2+7^2+51 =5 5 PC = 12^2+5^2 =13 q=P A=13-5 5 and p=P B=13+5 3 G.M. of p and q= p q = (13-5 5 )(13+5 5 ) = 169-125 =2 11 .

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