Find the center, vertices, and foci of the ellipse. Simplify your answers as much as possible. \( \frac{(x-5)^{2}}{169}+\frac{(y-3)^{2}}{25}=1 \)

In \( \triangle \mathrm{EFG}, e=96 \mathrm{~cm}, f=71 \mathrm{~cm} \) and \( \angle \mathrm{G}=52^{\circ} \). Find the length of \( g \), to the nearest centimeter.

In \( \triangle \mathrm{TUV}, u=4.8 \mathrm{~cm}, v=4.4 \mathrm{~cm} \) and \( \angle \mathrm{T}=84^{\circ} \). Find the length of \( t \), to the nearest 1oth of a centimeter.

In \( \triangle \mathrm{STU}, u=3.6 \) inches, \( s=7.9 \) inches and \( \angle \mathrm{T}=68^{\circ} \). Find the length of \( t \), to the nearest 10th of an inch.

In \( \triangle \mathrm{TUV}, u=750 \mathrm{~cm}, v=670 \mathrm{~cm} \) and \( \angle \mathrm{T}=160^{\circ} \). Find the length of \( t \), to the nearest centimeter.

Determine the standard equation of the ellipse using the stated information. Vertices of the major axis at \( (-1,9) \) and \( (-1,-11) \); length of the minor axis is 10 units. The standard equation of the ellipse is (Simplify your answer. Use integers or fractions for any numbers in the equation.)