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AP EAMCET20225 Jul 2022Evening ShiftMathematicsCircleActual

Suppose a circle passes through (0, a) and (b, h) having its centre at (c, 0) . Then the value of c is

Options

  1. Ab^2-a^2+h^2 2 b
  2. Bb^2+a^2-h^2 2 b
  3. Cb^2-a^2+h^2 2 a
  4. Db^2+a^2-h^2 2 a

Correct answer

A. b^2-a^2+h^2 2 b

Step-by-step solution

Let m be mid point of AB Coordinates of M are ( 0+b 2 , a+h 2 ) ( b 2 , a+h 2 ) OA ^2= AM ^2+ OM ^2( C -0)^2+(0-a)^2= ( b 2 -0 )^2+ ( a+h 2 -a )^2+ ( c-b 2 )^2+ (0- a+h 2 )^2 aligned C^2+a^2= b^2 4 + h^2 4 + a^2 4 - a h 2 + & c^2+ b^2 4 -b c + & a^2 4 + h^2 4 + a h 2 aligned C^2+a^2= a^2 2 + b^2 2 + h^2 2 +c^2-b c aligned & a^2 2 = b^2+h^2 2 -b c & -b c= a^2 2 - b^2+h^2 2 & c= a^2-b^2-h^2 -2 b & c= b^2-a^2+h^2 2 b aligned

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