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MHT CET2010MathematicsParabola

The equation of common tangent to the circle x²+y²=2 and the parabola y²=8 x is x+y-k . Then value of k is

Options

  1. A1
  2. B-1
  3. C2
  4. D-2

Correct answer

D. -2

Step-by-step solution

Given parabola is, y²=8 x Here, 4 a=8 a=2 Any tangent to the parabola is y=m x+ a m or m x-y+ 2 m =0 If it is a tangent to the circle x²+y²=2 , then length of perpendicular from centre (0,0) is equal to radius 2 . array lr & 2 / m m²+1 = 2 & 4 m² =2 (m²+1 ) & m⁴+m²-2=0 & (m²+2 ) (m²-1 )=0 array m²= 1 Hence, the common tangent are y= (x+2) . But given equation of tangent is x+y=k On comparing, we get k=-2

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