The given equation is that of an ellipse in the standard form ((x^2)/(a^2)) + ((y^2)/(b^2)) = 1. In this equation, the terms that are squared under the x and y are a^2 and b^2 respectively. In this case, a^2 = 49 and b^2 = 36.
This means that the length of the semi-major axis, a, is the square root of 49. The square root of 49 is 7, so a = 7.
Similarly, the length of the semi-minor axis, b, is the square root of 36. The square root of 36 is 6, so b = 6.
The distance from the center of the ellipse to the foci (c) is found using the formula c = sqrt(a^2 - b^2). This formula is derived from the property of ellipses that the sum of the distances from the foci to any point on the ellipse is constant and equal to the length of the major axis (2a).
Substituting the values we found for a and b into the equation for c, we get c = sqrt((7^2) - (6^2)).
So c = sqrt(49 - 36) = sqrt(13), which approximates to 3.605551275463989.
Therefore, the foci of the ellipse are located approximately 3.61 units from the center.