Use the equation c2 = a2 −b2 c 2 = a 2 − b 2 along with the given coordinates of the vertices and foci, to solve for b2 b 2. Substitute the values for a2 a 2 and b2 b 2 into the standard form of
The distance between one of the foci and the center of the ellipse is called the focal length and it is indicated by “c”. You need to know c=0 the ellipse would become a circle.The foci of an
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Find the equation of an ellipse centred at the origin with foci (0, ±5) and minor axis (12, 0). Solution: Given b = 12 and c = 5. Put these in the formula c 2 = a 2 – b 2 to find a. a 2 =
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Explanation: Find the equation of an ellipse with vertices (0, ± 8) and foci (0, ± 4). The equation of an ellipse is (x −h)2 a2 + (y − k)2 b2 = 1 for a horizontally oriented ellipse and
Find the equation of an ellipse passing through the origin with foci (±7, 0) and point (6, 2). Solution: Using the formula, we have 2a = 15.74 a = 7.87 Put a = 7.87 in c 2 = a 2 – b 2 to