The equation given is in the form of a circle’s equation in standard form, which is typically expressed as:
x² + y² = r²
In this case, we can see that the equation is:
x² + y² = 42
To find the center of the circle, we recall that the standard form of a circle centered at point (h, k) is:
(x - h)² + (y - k)² = r²
Here, (h, k) represents the coordinates of the center, and r is the radius of the circle.
In the given equation, the terms x² and y² imply that h = 0 and k = 0, as there are no additional terms subtracted from x or y. Thus, the center of the circle is at the origin:
(0, 0)
Moreover, we can determine the radius by taking the square root of the right-hand side of the equation:
r = √42
Summarizing, the center of the circle represented by the equation x² + y² = 42 is:
(0, 0)
This means that the circle is centered at the origin of the Cartesian plane.