Graph the ellipse and locate the foci.
\[
\frac{x^{2}}{49}+\frac{y^{2}}{25}=1
\]

Step 1 ：The given equation is of an ellipse. The standard form of an ellipse is \(\frac{x^{2}}{a^{2}}+\frac{y^{2}}{b^{2}}=1\), where \(a\) and \(b\) are the semi-major and semi-minor axes respectively. The foci of the ellipse are located at \((\pm c, 0)\) where \(c = \sqrt{a^{2}-b^{2}}\). In this case, \(a^{2} = 49\) and \(b^{2} = 25\), so \(a = 7\) and \(b = 5\). We can calculate \(c\) and then plot the ellipse and its foci.

Step 2 ：The foci of the ellipse are located at \(\boxed{(-4.898979485566356, 0)}\) and \(\boxed{(4.898979485566356, 0)}\). The graph of the ellipse and its foci is shown in the plot generated by the Python code.