The curve `x^2-y^2=5` and`x^2/18 +y^2/8=1` cut each other at any common point at an angle-

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

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

If the curves x^2-6x+y^2+8=0 and x^2-8y+y^2+16 -k =0 , (k gt 0) touch each other at a point , then the largest value of k is ________.

Find the value of p for which curves x^(2)=9p(9-y) and x^(2)=p(y+1) cut each other at right angles.

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

The curves y=4x^(2)+2x-8 and y=x^(3)-x+13 touch each other at the point

Show that the curves x y=a^2 and x^2+y^2=2a^2 touch each other.

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