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MHT CET2008MathematicsParabola

The equation of common tangent to the circle x²+y²=2 and parabola y²=8 x is

Options

  1. Ay=x+1
  2. By=x+2
  3. Cy=x-2
  4. Dy=-x+2

Correct answer

B. y=x+2

Step-by-step solution

Given, y²=8 x 4 a=8 a=2 Any tangent of parabola is, aligned y &=m x+ a m & m x-y+ 2 m =0 aligned If it is a tangent to the circle x²+y²=2 , then 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 = 1 Hence, the common tangents are y= (x+2) .

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