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If P and Q are the points of intersection of the circles x^2+y^2+3 x+7 y+2 p-5=0 and x^2+y^2+2 x+2 y-p^2=0 , then there is a circle passing through P, Q and (1,1) for

Options

  1. Aall values of p
  2. Ball except one value of p
  3. Call except two values of p
  4. Dexactly one value of p

Correct answer

A. all values of p

Step-by-step solution

Given circles S=x^2+y^2+3 x+7 y+2 p-5=0 S^ =x^2+y^2+2 x+2 y-p^2=0 Equation of required circle is S+ S^ =0 As it passes through (1,1) the value of = -(7+2 p) (6-p^2 ) If 7+2 p=0 , it becomes the second circle it is true for all values of p

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