Understanding the Formula for a Horizontal Ellipse: Explained Step by Step

Horizontal Ellipse Formula

The formula for a horizontal ellipse is given by:

((x-h)^2 / a^2) + ((y-k)^2 / b^2) = 1

In this formula:
– (h, k) represents the center of the ellipse

The formula for a horizontal ellipse is given by:

((x-h)^2 / a^2) + ((y-k)^2 / b^2) = 1

In this formula:
– (h, k) represents the center of the ellipse.
– a is the distance from the center to the vertices along the x-axis.
– b is the distance from the center to the vertices along the y-axis.

To understand this formula, let’s break it down step by step:

1. (x-h) represents the horizontal distance of any point (x, y) on the ellipse from the center along the x-axis.

2. Similarly, (y-k) represents the vertical distance of any point (x, y) on the ellipse from the center along the y-axis.

3. (x-h)^2 means that we are squaring the horizontal distance, which ensures that it is always positive.

4. Similarly, (y-k)^2 means that we are squaring the vertical distance, which is also always positive.

5. Dividing (x-h)^2 by a^2 means that we are scaling the horizontal distance by a, which determines how far the ellipse extends along the x-axis.

6. Dividing (y-k)^2 by b^2 means that we are scaling the vertical distance by b, which determines how far the ellipse extends along the y-axis.

7. When we add both of these scaled distances together, we get a sum equal to 1, indicating that the combined effect of the horizontal and vertical distances gives us an ellipse.

Remember that when a = b, the ellipse becomes a circle with a center at (h, k).

It’s important to note that the formula provided assumes that the major axis of the ellipse is parallel to the x-axis. If the major axis is parallel to the y-axis, then the formula would be:

((x-h)^2 / b^2) + ((y-k)^2 / a^2) = 1

That’s the formula for a horizontal ellipse.

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