When two circles intersects each other orthogonally, then 2(g1g2+f1f2)=c1c2 , where two circles are x2+y2+2g1x+2f1y+c1=0 and x2+y2+2g2x+2f2y+c2=0 Let c(h,k) be the centre of required circle which passes through (3,0) and also touches Y -axis ∴ Radius =√(h−3)2+(k−0)2=|h| ⇒(h−3)2+k2=h2 ⇒k2−6h+9=0 ...(i) Required circle (x−h)2+(y−k)2=h2 ⇒x2+y2−2hx−2ky+k2=0 ...(ii) ⇒g1=−h1,f1=−k,c1=k2 ∵ Circle (ii) is intersected orthogonally by x2+y2−6x+4y−3=0 ⇒g2=−3,f2=2,c2=−3 ∴2(g1g2+f1f2)=c1+c2 ⇒2[3h−2k]=−3+k2 ⇒6h−4k=−3+k2 ⇒k2−6h−3=−4k ⇒−9−3=−4k [from Eq. (i)] ⇒k=3 ∴32−6h+9=0 ⇒h=3 ∴ Center =(3,3) and from Eq. (ii) required circle is x2+y2−6x−6y+9=0