Given the circle x 2Y 2-6x-55 = 0, the moving circle m passes through the fixed point a (- 3,0) and is tangent to the known circle, the trajectory equation of the center m is obtained

Given the circle x 2Y 2-6x-55 = 0, the moving circle m passes through the fixed point a (- 3,0) and is tangent to the known circle, the trajectory equation of the center m is obtained

Let m (x, y) be the center of the moving circle and R be the radius. According to the nature of the inscribed circle, the length of the connecting line is equal to the difference between the radii of the two circles. That is: | Ma | = | R-R |, and because r = | MB |, so | Ma | - | MB | = + '- 8, and because the point B (- 3,0) outside the fixed circle, the center of the moving circle is outside the fixed circle