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Manipal MET2014MathematicsParabola

If the line y- 3 x+3=0 cuts the parabola y^2=x+2 at A and B , then P A P B is equal to where [where P=( 3 , 0)] .

Options

  1. A4(2- 3 ) 3
  2. B4( 3 +2) 3
  3. C4 3 3
  4. D2( 3 +2) 3

Correct answer

B. 4( 3 +2) 3

Step-by-step solution

Given P=( 3 , 0) Equation of line A B is x- 3 60^ = y-0 60^ =r aligned & x= 3 + r 2 , y= r 3 2 & point ( 3 + r 2 , r 3 2 ) lies on y^2=x+2 & & & 3 r^2 4 = 3 + r 2 +2 & - r 2 -(2+ 3 )=0 aligned Let the roots be r₁ and r₂ , then the product aligned r₁ r₂ & =P A P B= | -(2+ 3 ) 3 4 | & = 4(2+ 3 ) 3 aligned

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