%5E2%2B(y-6)%5E2%3D1-translated-4-left-2-up.jpeg "(x-16)^2+(y-6)^2=1 Translated 4 Left 2 Up")
Graphing a Circle
In this article, we will explore the equation (x-16)^2 + (y-6)^2 = 1 and its graphical representation.
What does the equation represent?
The equation (x-16)^2 + (y-6)^2 = 1 represents a circle in the Cartesian coordinate system. The center of the circle is located at the point (16, 6).
Translating the Circle
The equation (x-16)^2 + (y-6)^2 = 1 can be translated 4 units to the left and 2 units up by replacing x with x + 4 and y with y - 2. This gives us the new equation:
((x + 4) - 16)^2 + ((y - 2) - 6)^2 = 1
Simplifying the equation, we get:
(x - 12)^2 + (y - 8)^2 = 1
Graphing the Circle
To graph the circle, we can use the equation (x - 12)^2 + (y - 8)^2 = 1. The graph of the circle is shown below:
(insert graph here)
The circle has a center at (12, 8) and a radius of 1 unit.
Conclusion
In conclusion, the equation (x - 16)^2 + (y - 6)^2 = 1 represents a circle with a center at (16, 6) and a radius of 1 unit. By translating the equation 4 units to the left and 2 units up, we get a new equation (x - 12)^2 + (y - 8)^2 = 1 with a center at (12, 8).
