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JEE Advanced2008MathematicsCircleActual

Paragraph: A circle C of radius 1 is inscribed in an equilateral P Q R . The points of contact of C with the sides P Q, Q R, R P are D, E, F respectively. The line P Q is given by the equation 3 x+y-6=0 and the point D is ( 3 3 2 , 3 2 ) . Further, it is given that the origin and the centre of C are on the same side of the line P Q . Question: The equation of circle C is

Options

  1. A(x-2 3 )^2+(y-1)^2=1
  2. B(x-2 3 )^2+ (y+ 1 2 )^2=1
  3. C(x- 3 )^2+(y+1)^2=1
  4. D(x- 3 )^2+(y-1)^2=1

Correct answer

D. (x- 3 )^2+(y-1)^2=1

Step-by-step solution

Let centre of circle C be (h, k) . Then, | 3 h+k-6 3+1 |=1 3 h+k-6=2,-2 3 h+k=4 (Rejecting 2 because origin and centre of C are on the same side of P Q ) The point ( 3 , 1) satisfies Eq. (i). Equation of circle C is (x- 3 )^2+(y-1)^2=1 .

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