The ellipse in the standard \((x,y)\) coordinate plane below is the graph of \( \dfrac{(x-5)^2}{25} + \dfrac{(y-3)^2}{9} =1 \). Which of the following points are the foci of the ellipse?

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Given an ellipse in standard form:

$$ \frac{(x-h)^2}{a^2}+ \frac{(y-k)^2}{b^2} = 1 $$

The foci are \(c\) units away from the center along the major axis, where c is given by:

$$ c^2=a^2-b^2 $$ $$ c^2 = 25-9 $$ $$ c^2 = 16 $$ $$ c = 4 $$

The center is at \((5,3)\). Moving 4 away in the horizontal direction:

$$ (5\pm 4,3) $$ $$ (1,3) \text{ and } (9,3) $$