Prove that the curves `4x = y^2` and `4xy = k` cut at right angles if `k^2 = 512`.

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

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

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

Prove that the curves y^(2)=4axandxy=c^(2) cut at right angles if c^(4)=32a^(4)

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

The lines x+(k-1)y+1=0 and 2x+k^2y-1=0 are at right angles if

Find the condition that the curves 2x = y^2 and 2 xy = k may intersect orthogonally.

Prove that the tangents to the curve y = x^2-7x+12 at (3,0) and (4,0) are at right angles.

Show that all chords of the curve 3x^2 -y^2- 2x+ 4y= 0 , which subtend a right angle at the origin, pass through a fixed point. Find the co-ordinates of the point.