locus of centres of circles which touch two circles x^2 + y^2 = 16 and x^2 + y^2 = 16x externally

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C1: x2+y2=16C1: x2+y2=42center is 0,0 and radiusr1 is 4 units.C2:x2+y2-16x=0center is --162,0=8,0r2=-82+0-0=8Let radius of required circle C3 be h,k and radius be R.If two circles touch externally then center to center distance is equalto sum  of radii.For C1 and C3h-02+k-02=R+4R=h2+k2-4 ;iFor C2 and C3h-82+k-02=R+8R=h-82+k2-8 ;iiBy i and iih2+k2-4=h-82+k2-8h-82+k2-h2+k2=8-4h-82+k2-h2+k2=4Hence equation of locus of center of C3 will bex-82+y2-x2+y2=4

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