Prove that the curves x = y ^2 and xy = k cut at right angles if 8k ^2 = 1.
Prove that the curves x = y ^2 and xy = k cut at right angles if 8k ^2 = 1.

Given: Equations of the curves are  …..(i) and ……….(ii)

Substituting the value of  in eq. (ii), we get  

  

Putting the value of  in eq. (i), we get  

Therefore, the point of intersection  is = ……….(iii)

Differentiating eq. (i) w.r.t  

   ……….(iv)

Differentiating eq. (ii) w.r.t  

 ……….(v)

According to the question, 

 

 

 

   [From eq. (iii)]

   [Cubing both sides]