The locus of the midpoints of the chord of the circle, x2+y2=25 which is tangent to the  hyperbola, x29-y216=1 is

Equation of the chord having mid point h,k to the circle x2+y2=25 is hx+ky=h2+k2it can be written as y=−hkx+h2+k2kGiven this is tangent to the hyperbola x29−y216=1c2=a2m2-b2⇒h2+k2k2=9h2k2−16⇒h2+k22=9h2−16k2The locus is x2+y22=9x2-16y2   or    x2+y22-9x2+16y2=0