Question

Find the coordinates of the point at which the circles
x2 + y2 - 4x - 2y - 4 = 0 and x2 + y2 - 12x -- 8y-
12 = 0 touch each other. Also, find the equations
of common tangents touching the circle in distinct
points.​

Answer 1

Answer:

Please see the attachment

Answer 2

Answer:

Explanation:

point of intersection divides centers in the ratio of radii

center of circle1 = 2,1

center of circle2 = 6,4

radius of circle 1 =3

radius of circle 2 =14

therefore

points of intersection =46/17 , 26/17

now just find line joining their lines slope and the common tangents are inclined theta with line joining centers

slope of line inclined theta with other line = m+-tantheta / 1-+mtantheta