Question

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

Answer 1

AB = $r_1$+$r_2$, and hence touch externally and point of contact is (- 19/13 ,9/13) by ratio formula.

The common tangent is given by $S_1{S}_2$= 0 or 12x - 5y + 21 = 0 where

$S_1$and $S_2$are the equations of the circles in standard form.