Final answer:
The standard form of the equation of an ellipse is ((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1, where (h, k) represents the coordinates of the center, 'a' represents the length of the semi-major axis, and 'b' represents the length of the semi-minor axis.
Step-by-step explanation:
The standard form of the equation of an ellipse is given by:
((x-h)^2)/a^2 + ((y-k)^2)/b^2 = 1
Where (h, k) represents the coordinates of the center of the ellipse, 'a' represents the length of the semi-major axis, and 'b' represents the length of the semi-minor axis.
For example, if the center of the ellipse is (3, 4), the length of the semi-major axis is 5, and the length of the semi-minor axis is 3, the standard form of the equation would be:
((x-3)^2)/25 + ((y-4)^2)/9 = 1
Ellipses have fascinating properties in mathematics and geometry. They are geometric shapes defined by their characteristic elongated, oval-like appearance. An ellipse is a set of points where the sum of the distances from two fixed points (called the foci) to any point on the ellipse is constant.