what is the center of a circle represented by the equation $(x + 9)^2+(y - 6)^2 = 10^2$?\n$(-9,6)$\n$(-6,9)$\…
what is the center of a circle represented by the equation $(x + 9)^2+(y - 6)^2 = 10^2$?\n$(-9,6)$\n$(-6,9)$\n$(6,-9)$\n$(9,-6)$
Answer
Explanation:
Step1: Recall the standard form of a circle's equation
The standard form of a circle's equation is ((x - h)^2+(y - k)^2=r^2), where ((h,k)) is the center of the circle and (r) is the radius.
Step2: Rewrite the given equation in the standard form
The given equation is ((x + 9)^2+(y - 6)^2=10^2). We can rewrite ((x + 9)^2) as ((x-(-9))^2).
Step3: Identify the center ((h,k))
Comparing ((x-(-9))^2+(y - 6)^2=10^2) with ((x - h)^2+(y - k)^2=r^2), we get (h=-9) and (k = 6).
Answer:
((-9,6)) (i.e., the first option)