Show that `x + y + 1 = 0` touches the circle
`x^(2) + y^(2) -3x + 7y +14 = 0` and find its
point of contact.

Show that x = 7 and y = 8 touch the circle x^(2) + y^(2) - 4x - 6y -1 2 = 0 and find the points of contact.

Show that the tangent at (-1, 2) of the circle x^(2) + y^(2) - 4x -8y + 7 = 0 touches the circle x^(2) + y^(2) + 4x + 6y = 0 and also find its point of contact.

Show that the tangent at (-1, 2) of the circle x^(2) + y^(2) - 4x -8y + 7 = 0 touches the circle x^(2) + y^(2) + 4x + 6y = 0 and also find its point of contact.

Prove that the tangent at (3,-2) of the circle x^(2) + y^(2) = 13 touches the circle x^(2) + y^(2) + 2x - 10 y - 26 = 0 and find its point of contact.

Show that the line 3x+4y +20=0 touches the circle x^(2) + y^(2) =16 and find the point of contact

Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

Show that the line x + 2y - 4 = 0 touches the ellipse 3x^(2) + 4y^(2) = 12 also find the point of contact.

If x = 7 touches the circle x^2 + y^2 - 4x - y - 12 =0 , then the co-ordinates of the point of contact are :

Prove that the straight line y = x + a sqrt(2) touches the circle x^(2) + y^(2) - a^(2)=0 Find the point of contact.