To determine the center and radius of the given circles, compare the equations with the standard equation. For question a, the center is (-1, 3) and the radius is sqrt(5). For question b, the center is (0, 0) and the radius is sqrt(1/6). For question c, the center is (2, 5) and the radius is 3.
Question a:
To determine the center and radius of the circle represented by the equation (x + 1)² + (y - 3)² = 5, we can compare it with the standard equation of a circle (x - h)² + (y - k)² = r², where (h, k) is the center and r is the radius. By comparing the equations, we can see that the center of the circle is (-1, 3) and the radius is sqrt(5).
Question b:
To express the equation 5x² - y² +6=0 in a coordinate system with the origin at the center, we can divide the equation by 6 to obtain (5/6)x² - (1/6)y² + 1 = 0. Comparing this with the standard equation of a circle, we can determine that the center is at the origin (0, 0) and the radius is sqrt(1/6).
Question c:
To determine the center and radius of the circle represented by the equation x² + y² - 4x - 10y + 20 = 0, we can complete the square by rearranging the equation to (x² - 4x) + (y² - 10y) = -20. Completing the square for x and y, we get (x - 2)² + (y - 5)² = 9. Comparing this with the standard equation of a circle, we can determine that the center is (2, 5) and the radius is 3.