The moving circle is tangent to the fixed circle x ^ 2 + y ^ 2-6y = 0, and is tangent to the X axis. The trajectory equation of the center of the moving circle is obtained

The moving circle is tangent to the fixed circle x ^ 2 + y ^ 2-6y = 0, and is tangent to the X axis. The trajectory equation of the center of the moving circle is obtained

Let (x, y) be the center of the circle
→ x-0 = y (in the first quadrant)
0-x = y (second image time limit)
Another is that the tangent point is the coordinate origin
→x=0
All in all, there are three

The moving circle passes through the fixed point a (1,0) and is tangent to the circle (x + 1) ^ 2 + y ^ 2 = 16
What if the fixed point is a (2.0) and the circle is (x + 2) ^ 2 + y ^ 2 = 4?

The first problem is that two circles are inscribed, so the sum of the distances from the center of the moving circle to two fixed points a (1,0) and (- 1,0) is the radius 4 (fixed value) of the known circle, so it conforms to the definition of ellipse. Because a = 2, C = 1, (x ^ 2) / 4 + (y ^ 2) / 3 = 1 is the trajectory equation of the moving circle