(x-3)^2+(y-3)^2=8.75
What would be the transformations on this circle? I know the center is (3,3) so would it be vert. 3 up and horizontal 3 to the right? Or is it be different since it has a diameter.
correct. The radius has no effect on translation.
And the radius would also not be considered a separate translation? Such a a stretch?
To analyze the transformations of the equation (x-3)^2 + (y-3)^2 = 8.75, let's break down the equation to understand its components.
The standard equation of a circle is (x-h)^2 + (y-k)^2 = r^2, where (h, k) represents the center coordinates, and r represents the radius.
Comparing this with the given equation, we can see that the center coordinates are (3, 3). Therefore, the center of the circle is at the point (3, 3).
To determine the radius, we need to rewrite the equation in the standard form by isolating r^2.
(x-3)^2 + (y-3)^2 = 8.75
Rearranging the equation:
(x-3)^2 + (y-3)^2 = (sqrt(8.75))^2
(x-3)^2 + (y-3)^2 = 2.95
Now we can identify that the radius of the circle is √2.95 ≈ 1.715.
To understand the transformations, we compare the given equation to the standard form.
If we compare (x-3)^2 + (y-3)^2 = 2.95 to (x-h)^2 + (y-k)^2 = r^2, we can observe the following transformations based on the difference in values:
1. Horizontal translation: Since the sign for the x-component of the standard form equation is positive (x-h)^2, we can conclude that the circle has been shifted 3 units to the right (in the positive x-direction).
2. Vertical translation: The sign for the y-component of the standard form equation is also positive (y-k)^2, indicating that the circle has been shifted 3 units upwards (in the positive y-direction).
Therefore, the transformations on the given circle are a horizontal translation of 3 units to the right and a vertical translation of 3 units upwards from the standard form equation.