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AP EAMCET20227 Jul 2022Evening ShiftMathematicsCircleActual

The straight line touching the circle x^2+y^2-2 x-3=0 and remaining normal to the circle x^2+y^2-4 y-6=0 is

Options

  1. A4 x-3 y+6=0
  2. By+2=0
  3. C4 x+3 y-6=0
  4. D2 x+3=0

Correct answer

A. 4 x-3 y+6=0

Step-by-step solution

Line is normal to circle x^2+y^2-4 y-6=0 It passes through centre (0,2) . Let m be slope of line. Equation of line is y-2=m x m x-y+2=0 This line is tangent to x^2+y^2-2 x-3=0 centre is (1,0) , radius is 2 aligned & 2= | m+2 1+m^2 | & 4 (1+m^2 )=(m+2)^2 & 3 m^2-4 m=0 & m=0 & or m= 4 3 & aligned Line can be y=2 or 4 x-3 y+6=0

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