Vertical Ellipse Formula
The formula for a vertical ellipse can be written in general form as:
(x – h)^2 / a^2 + (y – k)^2 / b^2 = 1
where (h,k) represents the center of the ellipse, and a and b represent the semi-major and semi-minor axes, respectively
The formula for a vertical ellipse can be written in general form as:
(x – h)^2 / a^2 + (y – k)^2 / b^2 = 1
where (h,k) represents the center of the ellipse, and a and b represent the semi-major and semi-minor axes, respectively.
In this formula, (x – h)^2 represents the horizontal distance squared from the center of the ellipse, and a^2 represents the square of the semi-major axis. Dividing the horizontal distance squared by the square of the semi-major axis gives a value that determines how stretched or compressed the ellipse is in the x-direction.
Similarly, (y – k)^2 represents the vertical distance squared from the center of the ellipse, and b^2 represents the square of the semi-minor axis. Dividing the vertical distance squared by the square of the semi-minor axis gives a value that determines how stretched or compressed the ellipse is in the y-direction.
The constant value of 1 on the right side of the equation ensures that the sum of these values is always equal to 1, which maintains the elliptical shape.
It is important to note that the values of a and b determine the size and shape of the ellipse. The distance from the center of the ellipse to either focus is equal to c, where c^2 = a^2 – b^2. This value is useful for finding the foci, the vertices, and other important properties of the ellipse.
Overall, the vertical ellipse formula allows you to describe the shape, size, and position of an ellipse in a mathematical form.
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