we know that
X²+y²=9 -------> X²+y²=3²
is the equation of a circle with center (0,0) and radius r=3 units
so
the translation of four units to the right and three units down is equals to move the center (0,0)--------> (0+4,0-3)------> (4.-3)
the new center of the circle is (4,-3)
the new equation is
(x-4)²+(y+3)²=3²
see the attached figure