Prove that the line `x+y=3a` touches the curve `x^3+y^3=3axy`; 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.

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

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 straight line x + y=1 touches the hyperbola 2x ^(2) - 3y ^(2)= 6. Also 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.

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

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.

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