The circle (x + 2)2 + (y - 5)2 = 9. will be shifted 3 units up and 2 units to the right. what is the equation of the new circle?

From  (x + 2)2 + (y - 5)2 = 9 you can find that the circle middle point would be: (-2, 5)

If you shift it 3 units up (Y'= Y+3) and 2 unit right(X'= X+2) then the middle point will become: (-2+2, 5+3)= (0, 8)

Then the equation would be:
(x + 0)2 + (y - 8)2 = 9
x^2+ (y - 8)^2 = 9

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