Step-by-step explanation:
The circle of the center given center and a radius goes by the following pattern: (x - h)² + (y - k)² = r² in which (h, k) is the center and "r" is the radius.
Since the center (9, -16) is already given, this mean that h = 9 and k = -16.
In addition, radius r = 2. Plugging these values to the pattern above, we get: (x - 9)² + (y - (-16))² = 2²
Simplifying the equation above, we get:
(x - 9)² + (y + 16)² = 4
Answer:
In standard form, the equation of the circle is (x - 9)² + (y + 16)² = 4
In general form, we can eliminate the exponents by applying its property. We get:
(x² - 18x + 81) + (y² + 32y + 256) = 4
x² - 18x + 81 + y² + 32y + 256 = 4
Rearrange.
x² + y² - 18x + 32y + 81 + 256 - 4 = 0
x² + y² - 18x + 32y + 333 = 0
In general form, the equation of the circle is x² + y² - 18x + 32y + 333 = 0.