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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

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

Grade:12

1 Answers

Arun
25763 Points
3 years ago
Dear Aditya
 
 

x3/2+y3/2=A3/2, 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,x3/2+y3/2=A3/2, implies that x,y>0, thus, x=y=A(4)-1/3 is the one and only solution

 

Regards

Arun (askIITians forum expert)

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