Show that the circles `x^2+y^2-10 x+4y-20=0` and `x^2+y^2+14 x-6y+22=0` touch each other. Find the coordinates of the point of contact and the equation of the common tangent at the point of contact.

Prove that the circles x^(2) + y^(2) - 2x - 4y - 12 = 0 and 3x^(2) + 3y^(2) - 2x + 4y - 140 = 0 touch each other. Find the coordinates 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) + 6x + 14y + 9 = 0 and x^(2) + y^(2) - 4x - 10y - 7 = 0 touch each other externally, find also the equation of the common tangent of the two circles.

Prove that the circles x^(2) + y^(2) + 4x - 10y - 20 = 0 and x^(2) + y^(2) - 4x - 4y + 4 = 0 touch each other internally. Find the equation of their common tangent.

The circles x^2+y^2-12 x-12 y=0 and x^2+y^2+6x+6y=0. a.touch each other externally b.touch each other internally c.intersect at two points d.none of these

Show that the circles x^(2) + y^(2) + 6x + 2y + 8 = 0 and x^(2) + y^(2) + 2x + 6y + 1 = 0 intersect each other.

Find the locus of the point of intersection of the perpendicular tangents of the curve y^2+4y-6x-2=0 .

The tangent to the circle x^2+y^2=5 at (1,-2) also touches the circle x^2+y^2-8x+6y+20=0 . Find the coordinats of the corresponding point of contact.

Show that the circle x^(2) + y^(2) + 4(x+y) + 4 = 0 touches the coordinates axes. Also find the equation of the circle which passes through the common points of intersection of the above circle and the straight line x+y+2 = 0 and which also passes through the origin.