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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 
C1Cr1 + r2 
Thus, circles  touch each other internally

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