Give the equation for the new circle obtained by translating the circle (x − 2)" + (y + 4)" = 36 by 6 units to the right and 4 units up.

Question

I need some help please.

Answer 1

The equation for a circle translated a units to the right and b units up from the origin is:

(x - a)² + (y - b)² = r²

From this, we see that our circle is already translated 2 units to the right and 4 units down, so our new translation results in a circle translated 8 units to the right and 0 units vertically, or:

(x - 8)² + y² = 36