The calculated equation of the ellipse is x²/144 + y²/36 = 1
How to determine the equation of the ellipse.
From the question, we have the following parameters that can be used in our computation:
Center = (12, 0) and (0, 6)
The equation of an ellipse centered at the origin is represented as
x²/a² + y²/b² = 1
Using the point (12, 0), we have
12²/a² + 0²/b² = 1
12²/a² = 1
a = 12
Using the point (0, 6), we have
0²/a² + 6²/b² = 1
6²/b² = 1
b = 6
Recall that
x²/a² + y²/b² = 1
So, we have
x²/12² + y²/6² = 1
x²/144 + y²/36 = 1
Hence, the equation of the ellipse is x²/144 + y²/36 = 1
Question
The ellipse in the figure is centered at the origin and includes the points (12,0) and (0,6).
Find the equation of the ellipse.