show that the straight line `x/a+y/b=2` touches the curve `(x/a)^3+(y/b)^3=2` ; find the coordinates of the point of contact

Prove that the line x+y=3a touches the curve x^(3)+y^(3)=3axy; find the coordinates of the point of contact

Show that the straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also find the coordinates of the point of contact.

Prove that the line x+y=3a touches the curve x^(3)+y^(3)=3axy, find the coordinnates of the points of contact.

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 . Find the coordinates of the point of contact.

Show that the line 3x-4y=1 touches the circle x^(2)+y^(2)-2x+4y+1=0 . Find the coordinates of the point of contact.

Show that the line x + y + 1=0 touches the hyperbola x^(2)/16 -y^(2)/15 = 1 and find the co-ordinates of the point of contact.

Show that the straight line 3x + 4y = 20 touches the circle x ^2 + y ^2 = 16.

Show that the line y= x + sqrt(5/6 touches the ellipse 2x^2 + 3y^2 = 1 . Find the coordinates of the point of contact.

Show that the line y= x + sqrt(5/6 touches the ellipse 2x^2 + 3y^2 = 1 . Find the coordinates of the point of contact.

If the line x + y = 1 touches the parabola y^2-y + x = 0 , then the coordinates of the point of contact are: