How can you tell from the equation of an ellipse which is the major and minor axis?
2 answers
The major and minor axes are perpendicular to one another and are two axes of symmetry. For an ellipse, one is longer than the other. The major axis is the longer one. The major axis passes through the two foci of the ellipse.
Below is a typical ellipse equation.
[(x - 6)^2]/9 + [( y + 4)^2]/25 = 1
Do you see the denominators 9 and 25?
If you take the square root of each denominator, what is the biggest and smallest result?
The square root of 9 = 3.
The square root of 25 = 5.
From this we know that the smaller number 3 represents the minor axis and 5 (the bigger number) represents the major axis.
We also know, from the example above, that since the smaller number lies under the x coordinate, the minor axis is horizontal and the major axis is vertical for this equation. If 25 was the denominator of the x coordinate, then the minor axis would be vertical and the major axis would be horizontal.
Is this clear?
[(x - 6)^2]/9 + [( y + 4)^2]/25 = 1
Do you see the denominators 9 and 25?
If you take the square root of each denominator, what is the biggest and smallest result?
The square root of 9 = 3.
The square root of 25 = 5.
From this we know that the smaller number 3 represents the minor axis and 5 (the bigger number) represents the major axis.
We also know, from the example above, that since the smaller number lies under the x coordinate, the minor axis is horizontal and the major axis is vertical for this equation. If 25 was the denominator of the x coordinate, then the minor axis would be vertical and the major axis would be horizontal.
Is this clear?
3 answers