Question

Prove that the curves x - y² and xy = k cut at right angles if 8k² = 1.

Answer 1

x - y²      ......(i)

and  xy = k   .....(ii)

From (ii) y²y = k

or y³ = k

or y = k^1/3 

or x = k^2/3 

. ^.. (i) & (ii) cut at right angles.