Let the equation of the circle passing through (0,0) is x2+y2+2gx+2fy=0...(i) and the given equations are x2+y2+6x−15=0...(ii) x2+y2−8y−10=0...(iii) Eq(i) and (ii) are orthogonal. ∴2g×3+2f×0=0+(−15)...[∴2g1g2+2f1f2=c1+c2] ⇒g=−
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∴ Again Eq.(i)and(iii) are orthogonal ⇒2g×0+2f×(−4)=0+(−10) f=