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AP EAMCET202317 May 2023Morning ShiftMathematicsCircleActual

A circle S touches Y -axis at (0,3) and makes an intercept of length 8 units on X -axis. If the centre C of the circle S lies in the second quadrant, then the distance of C from the point (-2,-1) is

Options

  1. A13
  2. B10
  3. C5
  4. D2

Correct answer

C. 5

Step-by-step solution

Equation of circle touches y-axis at (0,3) is (x-a)^2+(y-3)^2=a^2 x^2+y^2-2 a x-6 y+9=a^2 Since the length of intercept on x -axis at this circle is 8 unit 2 a^2-9 =8 a^2=25 a= 5 Center lies in second co-ordinate a=-5 So, the centre is C(-5,3) Distance of the point (-2,-1) from C is (-2+5)^2+(-1-3)^2 = 9+16 =5

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