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MHT CET2011MathematicsParabola

The equation of the common tangent touching the circle (x-3)²+y²=9 and the parabola y²=4 x above the x -axis is

Options

  1. A2 y=3 x+1
  2. B3 y=-(x+3)
  3. C3 y=x+3
  4. D3 y=-(3 x+1)

Correct answer

C. 3 y=x+3

Step-by-step solution

Let the common tangent to the parabola array l y²=4 x be y=m x+ 1 m array It should be also touch the circle (x-3)²+y²=9 whose centre is (3,0) and radius =3 , then array cc & |3 m+1 / m| 1+m² =3 & 3 m²=1 & m= 1 3 array But m>0 , then equation of common tangent is y= 1 3 x+ 3 or 3 y=x+3

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