Prove that if curve `y=x^3` and `xy=k` cut each other orthogonally then `3k=1`

Prove that the curves y=x^(3) and xy-k cut each other orthogonally, if 3k= 1.

Prove that if the curves y=x^(3) and xy=K intersect orthogonally,then 3K=1

Prove that the curves 2y^(2)=x^(3) and y^(2)=32x cut each other orthogonally at the origin

Prove that the curve y=x^(2) and xy=k intersect orthogonally if 8k^(2)=1

If the curves y^(2)=4x and xy=a,a>0 cut orthogonally,then a is

Prove that the curves xy=4 and x^(2)+y^(2)=8 touch each other.

Show that the curve x^(3)-3xy^(2)=a and 3x^(2)y-y^(3)=b cut each other orthogonally, where a and b are constants.

If the curve ax^(2) + 3y^(2) = 1 and 2x^2 + 6y^2 = 1 cut each other orthogonally then the value of 2a :

Show that the curves 2x=y^(2) and 2xy=k cut each other at right angles if k^(2)=8

Prove that x^(2)-y^(2)=16 and xy=25 cut each other at right angles.