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AP EAMCET2012MathematicsCircle

A circle passes through the point (3,4) and cuts the circle x^2+y^2=a^2 orthogonally; the locus of its centre is a straight line. If the distance of this straight line from the origin is 25 , then a^2 is equal to

Options

  1. A250
  2. B225
  3. C100
  4. D25

Correct answer

B. 225

Step-by-step solution

Since, the circle passes through (3,4) and cuts the circle x^2+y^2=a^2 orthogonally. (x-3)^2+(y-4)^2=0 Also, x^2+y^2-a^2=0 Fquation of radical axis, aligned & (x-3)^2+(y-4)^2- (x^2+y^2-a^2 )=0 & x^2-6 x+9+y^2+16-8 y-x^2 & -y^2+a^2=0 & -6 x-8 y+25+a^2=0 & 6 x-8 y-25-a^2=0 aligned Now, the distance from (0,0) to Eq. (iii), we get aligned & |6(0)-8(0)-25-a^2 | 36+64 =25 & 25+a^2 10 =25 & 25+a^2=250 & a^2=225 & aligned

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