AP EAMCET Engineering 2012 Solved Paper

Since, the circle passes through (3,4) and cuts the circle x2+y2=a2 orthogonally.
∴ (x−3)2+(y−4)2=0 .......(i)
Also, x2+y2−a2=0 ........(ii)
∴ Equation of radical axis,
(x−3)2+(y−4)2−(x2+y2−a2)=0
⇒ x2−6x+9+y2+16−8y−x2 −y2+a2=0
⇒ 6x−8y+25+a2=0
⇒ 6x−8y−25−a2=0 ........(iii)
Now, the distance from (0,0) to Eq. (iii), we get

|6(0)−8(0)−25−a2|

√36+64

=25
⇒

25+a2

10

=25
⇒ 25+a2=250
⇒ a2=225