That's the definition of an ellipse.
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Yes the ratios are sometimes equal to each other.
Vertical Angles
You construct a Hexagon by drawing 8 lines that touch each other.
An ellipse is the set of each and every point in a place such that the sum of the distance from the foci is constant, Major Axis of the ellipse is the part from side to side the center of ellipse to the larger axis, or the length of that sector. The major diameter is the largest diameter of an ellipse. Below equation is the standard ellipse equation: X2/a + Y2/b = 1, (a > b > 0)
Each of them is precisely equal to the other.