The general equation of the circle is given by:
x2 + y2 + 2gx + 2fy + c = 0
centre is (-g, -f) radius = √g2+ f2 - c
We know that the condition of circles to touch internally or externally depends upon the distance between its centres and sum of its radius.
If C1C2 > r1 + r2 then circlesdon't touch each other.
If C1C2 = r1 + r2 then circles touch each other externally
If C1C2 < r1 + r2 then circles touch each other internally
In the given question,
C1 = (-1, 0), C2 = (3, -3) , r1 = 3, r2 = √62
C1C2 = √ 16 + 9 = 5
Now from the above equation
C1C2 < r1 + r2
Thus, circles touch each other internally