The equation of an ellipse that has its major axis oriented vertically differs slightly from the standard form in that the terms a and b, which represent the lengths of the semi-major and semi-minor axes respectively, is swapped around.
It is given by...
\frac{x^2}{b^2} + \frac{y^2}{a^2} = 1
Notice that the semi-major axis a, now sits under y, the vertical coordinate.
Similarly, the coordinates and relationships for the features of the ellipse are also switched around:
The x-intercepts are given by: (±b, 0)
The y-intercepts are given by: (0, ±a)
The foci are given by: (0, ±ae)
The directrices are given by: (0, ±a/e)
In this video, we go through the following examples:
- Sketching the ellipse x2/49 + y2/64 = 1 and defining all features
- Sketching the ellipse (x-1)2/4 + (y+2)2/16 = 1 and defining all features
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