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AP EAMCET202423 May 2024Morning ShiftMathematicsCircleActual

The circumference of a circle passing through the point (4,6) with two normals represented by 2 x-3 y+4=0 and x+y-3=0 is

Options

  1. A5
  2. B10
  3. C25
  4. D8

Correct answer

B. 10

Step-by-step solution

Intersection of two normals will be the centre of the circle. 2 x-3 y+4=0 ....(i) and x+y-3=0 ....(ii) Solving equations (i) and (ii) we get, Centre =(1,2) Also, circle passes through (4,6) Radius (r)= (4-1)^2+(6-2)^2 =5 So, circumference =2 r=10 .

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