Horizontal Ellipse Formula
The equation of a horizontal ellipse is given by:
[(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 equation of a horizontal ellipse is given by:
[(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.
To visualize this equation, let’s break it down:
The term (x – h)^2 represents the squared distance of any point (x, y) on the ellipse from the center’s x-coordinate. Similarly, the term (y – k)^2 represents the squared distance of the point from the center’s y-coordinate.
The values within the square brackets, a^2 and b^2, represent the squares of the semi-major and semi-minor axes, respectively. These values determine the size and shape of the ellipse.
The division sign (/) indicates that the summed squared distances from the center should be divided by the squares of the semi-axes.
Finally, the equal sign with the value 1 on the right side denotes that the sum of the two terms within the brackets should be equal to 1, creating an ellipse.
To graph a horizontal ellipse, you can follow these steps:
1. Determine the center of the ellipse, (h, k).
2. Calculate the values of a and b, which represent the semi-major and semi-minor axes.
3. Plot the center coordinates (h, k) on the Cartesian plane.
4. Use the values of a and b to determine the distance from the center along the x and y axes to mark the end points of the major and minor axes.
5. Sketch the ellipse by connecting the end points of the major and minor axes smoothly.
Remember, the shape of the ellipse will vary depending on the ratio of a to b. If a = b, you will have a circle. If a > b, the ellipse will be stretched more horizontally, and if a < b, the ellipse will be stretched more vertically. I hope this explanation helps you understand the formula and how to graph a horizontal ellipse. Feel free to ask any further questions!
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