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AP EAMCET202316 May 2023Evening ShiftMathematicsCircleActual

The lengths of the intercepts made by a circle S on X and Y - axes are 2 13 3 and 2 22 3 respectively. If the radius of the circle S is 38 3 and its centre C lies in the second quadrant, then C =

Options

  1. A( -5 3 , 4 3 )
  2. B( -4 3 , 5 3 )
  3. C( -6 5 , 7 5 )
  4. D( -7 5 , 6 5 )

Correct answer

B. ( -4 3 , 5 3 )

Step-by-step solution

Let equation of the circle be x^2+y^2+2 g x+2 f y+c=0 ... (i) Now length of intercepts made by x axis is 2 g ^2- c = 2 13 3 g ^2- c = 13 9 ... (ii) Similarly, 2 f ^2- c = 2 22 3 f ^2- c = 22 9 ... (iii) Since, radius = 38 3 aligned & g ^2+ f ^2- c = 38 3 g ^2+ f ^2- c = 38 9 & 13 9 + 22 9 + C = 38 9 (by (ii) & (iii)) & C = 3 9 = 1 3 aligned So g ^2= 13 9 + 1 3 = 16 9 g = 4 3 & f ^2= 22 9 + 1 3 = 25 9 f = 5 3 Since centre lies in 2nd quadrant so centre = (- 4 3 , 5 3 )

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