Determine the centre of the circle and the length of the radius in the following:
a. (x - 2)^2 + (y + 1)^2 = 5
b. 2(x + 1)^2 + 2y^2 = 8
a. The equation of the circle is given in the form (x - h)^2 + (y - k)^2 = r^2, where (h, k) is the center of the circle and r is the radius.
In the given equation, (x - 2)^2 + (y + 1)^2 = 5, we can see that the center of the circle is (2, -1) and the radius is √5.
Therefore, the center of the circle is (2, -1) and the length of the radius is √5.
b. To determine the center and radius of the circle, we need to convert the equation to the standard form (x - h)^2 + (y - k)^2 = r^2.
Starting with 2(x + 1)^2 + 2y^2 = 8, we divide both sides by 2 to simplify the equation:
(x + 1)^2 + y^2 = 4
Comparing this equation to the standard form, we can see that the center of the circle is (-1, 0) and the radius is 2.
Therefore, the center of the circle is (-1, 0) and the length of the radius is 2.