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AP EAMCET2016MathematicsCircle

A circle S=0 with radius 2 touches the line x+y-2=0 at (1,1) . Then, the length of the tangent drawn from the point (1,2) to S=0 is

Options

  1. A1
  2. B2
  3. C3
  4. D2

Correct answer

C. 3

Step-by-step solution

Equation of line at (1,1) is x+y-2=0 Slope of this line is -1 . So, slope of line perpendicular to this line is 1 . =1 = 4 Let, centre of circle (h, k) i.e. x=h r and y=k r As, it passes through (1,1) . aligned & h=1 2 4 & k=1 2 4 & h=1 2 2 and k=1 2 2 & h=2,0 and k=2,0 aligned Centres are (2,2) or (0,0) Hence, equation of circle x^2+y^2=2 or (x-2)^2+(y-2)^2=2 Length of tangent from (1,2)= 1^2+2^2-2 = 3

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