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Manipal MET2015MathematicsParabola

Two common tangents to the circle x^2+y^2=2 a^2 and parabola y^2=8 a x are

Options

  1. Ax= (y+2 a)
  2. By= (x+2 a)
  3. Cx= (y+a)
  4. Dy= (x+a)

Correct answer

B. y= (x+2 a)

Step-by-step solution

The equation of any tangent to y^2=8 a x is y=m x+ 2 a m ...(i) If it touches x^2+y^2=2 a^2 , then ( 2 a m )^2=2 a^2 (1+m^2 ) [ c^2=a^2 (1+m^2 ) ] 2=m^2 (m^2+1 ) array rlrl & m^4+m^2-2 & =0 & (m^2+2 ) (m^2-1 ) & =0 & & m^2-1 & =0 & & m & = 1 array Putting the values of m in Eq. (i), we get y= (x+2 a) as the equations of common tangents.

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