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AP EAMCET2014MathematicsCircle

The length of the common chord of the two circles x^2+y^2-4 y=0 and x^2+y^2-8 x-4 y+11=0 , is

Options

  1. A145 4 ~cm
  2. B11 2 ~cm
  3. C135 ~cm
  4. D135 4 ~cm

Correct answer

D. 135 4 ~cm

Step-by-step solution

Given equation of circles are and gathered x^2+y^2-4 y=0 x^2+y^2-8 x-4 y+11=0 gathered Equation of chord aligned & x^2+y^2-4 y- (x^2+y^2-8 x-4 y+11 )=0 & 8 x-11=0 aligned Centre and radius of first circle are O(0,2) and O P=r=2 . Now, perpendicular distance from O(0,2) to the line 8 x-11 is d=O M= |8 0-11| 8^2 = 11 8 In O M P , aligned P M & = O P^2-O M^2 & = 2^2- ( 11 8 )^2 & = 4- 121 64 = 256-121 64 & = 135 8 aligned Length of chord P Q=2 P M=2 135 8 = 135 4 ~cm

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