Question

write an equation for the translation of x^2+y^2=25 by 6 units left and 3 units down

Answer 1

The initial center given by the initial equation is (0, 0).

Translated 6 units left and 3 units down makes the new center as (-6, -3).

Since we know that (h, k) represents the center of a circle, simply plug that into the long equation of a circle to get your equation.

\[(x - h)^2 + (y - k)^2 = r^2\]
(h, k) = (-6, -3)

\[(x + 6)^2 + (y + 3)^2 = 25\]
Note that the radius doesn't change at all since only the position of the circle changes, not the size/dimensions of it.

Answer 2

thanks that helped