Question

Please answer at least one of them

Answer 1

The equation of a circle with radius r and center at point (a, b) is given by
(x - a)^2 + (y - b)^2 = r^2
1.) For the circle given by x^2 + y^2 = 24
(x - 0)^2 + (y - 0)^2 = (√24)^2
Therefore, center = (0, 0) and radius = √24 = 4.9 units

3.) x^2 + y^2 -10x -2y = -10
x^2 - 10x + (-5)^2 + y^2 - 2y + (-1)^2 = -10 + (-5)^2 + (-1)^2
x^2 - 10x + 25 + y^2 - 2y + 1 = -10 + 25 + 1
(x - 5)^2 + (y - 1)^2 = 16
(x - 5)^2 + (y - 1)^2 = 4^2