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AP EAMCET2004MathematicsCircle

A line l meets the circle x^2+y^2=61 in A, B and P(-5,6) is such that P A=P B=10 . Then, the equation of l is

Options

  1. A5 x+6 y+11=0
  2. B5 x-6 y-11=0
  3. C5 x-6 y+11=0
  4. D5 x-6 y+12=0

Correct answer

C. 5 x-6 y+11=0

Step-by-step solution

Since, the line l meets the circle x^2+y^2=61 at two points A and B . P A=P B=10 P M is perpendicular to A B and O M is perpendicular to the chord A B , therefore line O P is perpendicular to A B . The slope of line P O is - 6 5 . Now, taking option (c). Let the required line be 5 x-6 y+11=0 its slope is 6 5 . Now, 5 6 (- 5 6 )=-1 Therefore our assumption is true.

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