Question
Prove that the curves x = y2 and xy = k cut at right angles if 8k2 = 1.
Solution
The equation of two curves are
x = y2 ...(1)
and xy = k ...(2)
From (1) and (2), 
From (2), 
At 
Curves (1) and (2) cut at right angles if 
i.e., 
Hence the result.
