the number of tangents to the curve x^3/2+y^3/2=a^3/2 where tangents are equally inclined to the axes is,

a)2

b)1

c)0

d)4

x^3/2+y^3/2=A^3/2, differentiating both sides w.r.t. x, (3/2)√x +(3/2)√y(dy/dx)=0

dy/dx=-√(x/y), therefore if tangent is equally inclined to axes, mod(dy/dx)=1, in addition,x^3/2+y^3/2=A^3/2, implies that x,y>0, thus, x=y=A(4)^-1/3 is the one and only solution

Regards

Arun (askIITians forum expert)