Concept:Use implicit differentiation twice on xm+ym=k and compare the second derivative with the given form.Explanation:Given xm+ym=k, differentiate with respect to x.mxm−1+mym−1y′=0y′=−ym−1xm−1Differentiate again to get y′′.y′′=−(m−1)(ym−1xm−2+y2m−1x2m−2)Taking the common denominator y2m−1,y′′=−(m−1)y2m−1xm−2(xm+ym)Since xm+ym=k,y′′=y2m−1(1−m)kxm−2Compare with y′′=ycaxb.a=(1−m)k,b=m−2,c=2m−1Given a+b+c=0,(1−m)k+(m−2)+(2m−1)=0(1−m)k+3m−3=0(1−m)(k−3)=0Since m=1, we get k=3.Answer:k=3, so the correct option is C.