Question

circles
try another translation using the circle from the previous problem.
think about it
do you remember the equation for a circle with its center located at the origin?
write an equation for the translation of ( x^2 + y^2 = 9 ) eight units to the right and four units down. then graph the translation.
a. ( (x - 8)^2 + (y - 4)^2 = 3 )
b. ( (x - 8)^2 + (y + 4)^2 = 9 )
c. ( (x - 8)^2 + (y + 4)^2 = 3 )
d. ( (x - 8)^2 + (y - 4)^2 = 9 )

Explanation:

Step1: Identify original circle parameters

The original circle equation is $x^2 + y^2 = 9$, so its center is $(0,0)$ and radius $r = \sqrt{9} = 3$.

Step2: Apply horizontal translation

Translate 8 units right: new $x$-coordinate of center is $0 + 8 = 8$.

Step3: Apply vertical translation

Translate 4 units down: new $y$-coordinate of center is $0 - 4 = -4$.

Step4: Write translated circle equation

Use the standard circle formula $(x-h)^2 + (y-k)^2 = r^2$, where $(h,k)=(8,-4)$ and $r=3$.
Expression: $(x-8)^2 + (y-(-4))^2 = 3^2$ which simplifies to $(x-8)^2 + (y+4)^2 = 9$.

Answer:

B. $(x-8)^2 + (y+4)^2 = 9$