Find the equation of the circle that is shifted 5 units to the left and 2 units down from the circle with the equation x^2+y^2=19.

Shifting a circle results to changes in the coordinates of the circle. For instance, if the coordinates of the center of the circle is taken to be (0,0), the new coordinates will be [(0+5),(0+2)] after shifting. The equation of the circle will also change with the same margin.

That is, the new equation will be;
(5+x)^2+(2+y)^2 =19

Notice, only the coordinates changes.