The ellipse with the equation stated above is:
Position I (Option C )
What is an Ellipse in Maths?
An ellipse is a circle that has been extended in one direction such that it is no longer a circle but an oval.
Solution
In order to determine the position of the ellipse with the above equation, we can start by simplifying the equation.
Hence, 9x² + 16y = 144 becomes
x²/16 + y²/9 = 1 (We arrive at this by dividing both sides of the equation by 144);
The x-axis is the major axis because the biggest denominator is under the x² term.
Thus the coordinates of the vertices are as follows:
(± a, 0); (0, ± b)
Hence:
a² = 16 → a = 4
b² = 4 → b = 2
Hence the coordinates are:
(± 4, 0); (0, ± 2)
Given the above, the eccentricity is given as:
e = √(1 - (3/4)^2 = (√7)/4 = 0.6614378
Hence the ellipse is: 0.66
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