Translate the circle x^2+y^2-4y=49 by the vector (3,-5). Write an equation for the image circle.

Question

Please help me get the answer please.

Answer 1

x² + y² - 4y = 49 

x² + y² - 4y + 4 = 49 + 4       complete the square

(x + 0)² + (y - 2)² = 53          graphing form

(x + 0 + 3)² + (y - 2 - 5)² = 53  translate

(x + 3)² + (y - 7)² = 53              simplify