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Find the equation of ellipse with center C(0, 4), foci F1(0, 0) and F2(0, 8), and major axis of length 10 units.
Solution:
To illustrate the problem, it is better to draw the figure as follows
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| Photo by Math Principles in Everyday Life |
If the coordinates of the center and foci and the length of major axis are given, then c = 4, and a = 10/2 = 5. The value of b is
Since the coordinates of the foci have the same x-coordinate, then the major axis is parallel to y-axis. Therefore, the equation of ellipse whose center is C(h, k) in standard form is
In general form, the equation of ellipse is
