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AP EAMCET202423 May 2024Morning ShiftMathematicsCircleActual

If (1,3) is the midpoint of a chord of the circle, x^2+y^2-4 x-8 y+16=0 , then the area of the triangle formed by that chord with the coordinate axes is

Options

  1. A16
  2. B8
  3. C4
  4. D8 2

Correct answer

B. 8

Step-by-step solution

Circle : x^2+y^2-4 x-8 y+16=0 Equation of chord with given middle point (1,3) is aligned & T=S₁ x+3 y-2(x+1)-4(y+3)+16 & =1+9-4-24+16 & x+y=4 aligned It cuts co-ordinate axes at A(0,4) and B(4,0) A O B is right angle. Area = 1 2 O A O B= 1 2 4 4=8

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