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AP EAMCET201726 Apr 2017Morning ShiftMathematicsCircleActual

If a circle with radius 2.5 units passes through the points (2,3) and (5,7) , then its centre is

Options

  1. A(1.5, 2)
  2. B(7, 10)
  3. C(3, 4)
  4. D(3.5, 5)

Correct answer

D. (3.5, 5)

Step-by-step solution

Let centre of the circle be c(x, y) . Here, C A and C B both represents the radius of the circle. So, it will be equal. Then, C A=C B array cc & C A^2=C B^2 & (5-x)^2+(7-y)^2=(2-x)^2+(3-y)^2 & 25+x^2-10 x+49+y^2-14 y & =4+x^2-4 x+9+y^2-6 y & 74-13=6 x+8 y & 6 x+8 y=61 array This equation is satisfied by the coordinates given in option (d).

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