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MHT CET2007MathematicsCircle

A line is drawn through a fixed point P( , ) to cut the circle x²+y²=r² at A and B . Then P A P B is equal to

Options

  1. A( + )²-r²
  2. B²+ ²-r²
  3. C( - )²+r²
  4. DNone of the above

Correct answer

B. ²+ ²-r²

Step-by-step solution

The equation of any line through the point P( , ) is x- = y- =k (say) Any point on this line is ( +k , +k ) This point lies on the given circle, if ( +k )²+( +k )²=r² or k²+2 k( + ) + ²+ ²-r²=0 Which being quadratic in k , gives two values of k . Let P A=k₁, P B=k₂ , where k₁, k₂ are the roots of Eq. (i), then P A P B=k₁ k₂= ²+ ²-r²

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