show that `x-2y+1=0` touches the hyperbola `x^2-6y^2=3`

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.

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

If the line 2x+sqrt6y=2 touches the hyperbola x^2-2y^2=4 , then the point of contact is

The st. line y = 4x + c touches the hyperbola x^2-y^2=1 if .

The point of contact of 5x+6y+1=0 to the hyperbola 2x^(2)-3y^(2)=2 is

The point of contact of 5x+6y+1=0 to the hyperbola 2x^(2)-3y^(2)=2 is

Find the value(s) of k so that the line 2x+y+k=0 may touch the hyperbola 3x^(2)-y^(2)=3