Find the following trajectory equation (1) for the center of circle m and circle C: (x + 2) &# 178; + Y & # 178; = 2, which is inscribed and passes through point a (2,0)

Find the following trajectory equation (1) for the center of circle m and circle C: (x + 2) &# 178; + Y & # 178; = 2, which is inscribed and passes through point a (2,0)

Distance from m to fixed point (2,0) - distance difference from m to fixed point (- 2,0) = √ 2
The trajectory of M is the left branch of hyperbola
2a=√2
a=√2/2
c=2
b²=4-1/2=7/2
Ψ m trajectory:
x²/(1/2)-y²/(7/2)=1,(x<=-√2/2)

Circle X & # 178; + Y & # 178; - 2x-4y-4 = 0, center coordinate is, radius is

X-x-y-2x-4y-4 = 0
(x-1) x (Y-2) = 9
Center of circle (1,2)
Radius 3