Why Is the Y-Axis the Major Axis When b > a in an Ellipse Equation?

Therefore, if b > a, then y is the major axis because b is the larger value and represents the distance from the centre to the furthest point on the ellipse. Conversely, if a > b, then x is the major axis. This is why the opposite is true in the equation: \frac{x^2}{a^2} + \frac{y^2}{b^2} = 1. In summary, the major axis of an ellipse is determined by the larger value between a and b in the equation, with the minor axis being the smaller value.
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This is a really dumb question, but could someone quickly explain why it is that if b > a in the equation of an ellipse then y is the major axis. Just intuitively I want to think that y^2/5 as opposed to y^2/3 is going to be smaller for a given value of y since each value is being limited by the dividend. The opposite is true. Can someone explain this simply?
 
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[itex]\frac{x^2}{a^2}+\frac{y^2}{b^2}=1[/itex]

The distance [itex]r[/itex] of every point of the ellipses from the centre of the frame of reference is always between [itex]min(a,b)\leq r\leq max(a,b)[/itex].
By definition, the major axis is defined as [itex]max(a,b)[/itex] while the minor axis is [itex]min(a,b)[/itex].
 

FAQ: Why Is the Y-Axis the Major Axis When b > a in an Ellipse Equation?

1. What is an ellipse?

An ellipse is a geometric shape that resembles a flattened circle. It is defined as a curve in which the sum of the distances from any point on the curve to two fixed points (called the foci) is constant.

2. How is an ellipse different from a circle?

An ellipse is different from a circle in that it has two foci, while a circle only has one. The shape of an ellipse is also elongated, while a circle is perfectly round.

3. What causes confusion about ellipses?

Confusion about ellipses often arises because they are similar to circles, but have slightly different properties. Additionally, the terminology used to describe ellipses, such as "major axis" and "minor axis," can be confusing.

4. How are ellipses used in science?

Ellipses are used in many fields of science, including astronomy, physics, and engineering. They are used to describe the orbits of planets and other celestial bodies, as well as to model the trajectories of satellites and other objects in space.

5. Can an ellipse have a negative value?

No, an ellipse cannot have a negative value. The dimensions of an ellipse, such as its major and minor axes, are always positive. However, the orientation of an ellipse can be described as clockwise or counterclockwise, which may be interpreted as negative or positive.

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