The equation you've provided is of a circle, specifically it's in the standard form of the equation of a circle. The general form is as follows:
(X-a)² + (Y-b)² = r²
In this formula, 'a' and 'b' are the x, and y coordinates of the center of the circle, and 'r' is the radius.
From the provided equation which is, (X+1)² + Y² = 49, The term with X is (X+1) and with Y is just Y. As these terms are of the form (X-a) and (Y-b), we can equate and find that:
a = -1 (From X+1 i.e. X-(-1))
b = 0 (Since there's no Y term or rather we can consider it as Y-0)
So, the center of the circle is at the coordinate (-1,0).
Now, to find the radius, we know that in the equation of a circle, the constant on the right side equals to the square of the radius of the circle. Here, the constant is 49. So, r² = 49, which gives us r = √49.
Calculating the square root of 49, we find r = 7.
Therefore, we have found that the center of the circle is at (-1,0) and the radius of the circle is 7.