An ellipse has a major axis length of 10 and a minor axis length of 6. Find the coordinates of its center if it is centered at the origin.

The center of an ellipse that is centered at the origin is simply at the coordinates (0, 0). With a major axis length of 10, that means the semi-major axis is 5, and for a minor axis length of 6, the semi-minor axis is 3. Hence, the equation of the ellipse can be expressed as \(\frac{x^2}{25} + \frac{y^2}{9} = 1\). On your mathematical adventure, remember that ellipses can be found in a variety of real-world situations! From the orbits of planets around stars to design layouts in architecture, their elliptical shapes can optimize structure and aesthetics. Engineers often use elliptical shapes to maximize strength in bridges while minimizing material use, depicting yet another way mathematics intertwines with practical applications in our lives.