Understanding the Equation of a Vertical Ellipse: Explained with Formulas, Definitions, and Properties

Vertical Ellipse Formula

The equation of a vertical ellipse is given by:

(x – h)^2 / a^2 + (y – k)^2 / b^2 = 1

where (h, k) represents the center of the ellipse, “a” is the length of the major axis (the distance from the center to the farthest point on the ellipse), and “b” is the length of the minor axis (the distance from the center to the closest point on the ellipse)

The equation of a vertical ellipse is given by:

(x – h)^2 / a^2 + (y – k)^2 / b^2 = 1

where (h, k) represents the center of the ellipse, “a” is the length of the major axis (the distance from the center to the farthest point on the ellipse), and “b” is the length of the minor axis (the distance from the center to the closest point on the ellipse).

In this equation, the denominators a^2 and b^2 denote the squares of the semi-major axis (a) and semi-minor axis (b), respectively.

The difference between the major and minor axes can be visualized as follows:

– The major axis is the longer of the two axes.
– The minor axis is the shorter of the two axes.

For a vertical ellipse, the major axis is oriented vertically (up and down) and the minor axis is oriented horizontally (left and right).

The values of a and b determine the shape of the ellipse. If a > b, then the ellipse is stretched more vertically, and if b > a, then the ellipse is stretched more horizontally.

It’s important to note that in the above equation, the constant on the right side of the equation is always 1. If this constant were to be different (e.g., 2 or 3), the equation would represent an ellipse with a different eccentricity from a perfect circle.

Overall, the equation of a vertical ellipse allows us to express the relationship between the coordinates (x, y) of any point on the ellipse, the position of the center (h, k), and the lengths of the major and minor axes (a, b).

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