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AP EAMCET201823 Apr 2018Evening ShiftMathematicsParabolaActual

The equation of one of the common tangents of the circle x^2+y^2-6 y+4=0 and the parabola y^2=x is

Options

  1. A2 x-y+1=0
  2. B2 x-y=1
  3. C4 x-y+1=0
  4. Dx-2 y+1=0

Correct answer

D. x-2 y+1=0

Step-by-step solution

Let the equation of tangent to the parabola y^2=x , having slope m is, y=m x+ 1 4 m For common tangent to the circle x^2+y^2-6 y+4=0 Radius 9-4 = |3- 1 4 m | 1+m^2 array rlrl & 5 (1+m^2 ) & =9+ 1 16 m^2 - 3 2 m & & m & = 1 2 array So, equation of common tangent is aligned y & = 1 2 x+ 1 2 x-2 y+1 & =0 . aligned

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