Show that the two circles `x^(2) + y^(2) - 4x + 10y + 20 = 0 ` and ` x^(2) + y^(2) + 8x - 6y - 24 =0 ` touch each other . Also , find co-ordinates of their point of contact .

Show that the two circles x^(2) + y^(2) + 4x - 12 y + 4 = 0 and x^(2) + y^(2) - 2x - 4y + 4 = 0 touch each other . Also , find the co-ordinates of the point of contact .

Show that the circles x^(2) + y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch each other externally, find the coordinates of their point of contact.

Show that the circles x^(2) + y^(2) - 8x - 4y - 16 = 0 and x^(2) + y^(2) - 2x + 4y + 4 = 0 touch each other internally and find the coordinates of their point of contact.

Show that the circles x^(2) +y^(2) - 2x - 4y - 20 = 0 and x^(2) + y^(2) + 6x +2y- 90=0 touch each other . Find the coordinates of the point of contact and the equation of the common tangent .

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

Prove that the circles x^(2) +y^(2) - 4x + 6y + 8 = 0 and x^(2) + y^(2) - 10x - 6y + 14 = 0 touch at the point (3,-1)

Show that the circles x^(2) + y^(2) + 2 x -6 y + 9 = 0 and x^(2) +y^(2) + 8x - 6y + 9 = 0 touch internally.

Show that the circles x^(2) + y^(2)-4x-6y-12=0 and x^(2) +y^(2) + 6x + 18 y + 26 = 0 touch each other. Also find the point of contact and common tangent at this point of contact.