# Find the major axis of an ellipse

• dE_logics
In summary, the conversation discusses finding the value of 'a' or half of the major axis of an ellipse using knowledge of its circumference and length of the minor axis. The equation used is derived from the circumference formula and results in four possible values for x, which can then be used to solve for the major axis. There is some confusion regarding the use of the symbol %x3, but the final result obtained using goal seek is deemed correct.
dE_logics
I want to figure out the 'a' of an ellipse (i.e. (major axis)/2) by knowledge of it's circumference and length of minor axis.

Using my little knowledge which I gained from reading (roughly) the ellipse article of wikipedia; I realized that I need to use that notorious and approximate circumference formula...so I made an equation to derive the 'a' or half of the major axis which needs to be solved.

quickmath.com gave 4 results so as to turn my vertical scroll bar into a tiny line (try it yourself, I'll post the equation).

Axiom suggest a syntax error which I know it not true, I think it has given up.

This is the equation -

h=((22/7)*(x+(c/2))*(1+(((3*((x-(c/2))/(x+(c/2)))^2))/(10+(4-(3*((x-(c/2))/(x+(c/2)))^2))^(1/2)))))/2

Which obviously I've converted from human readable format.

You need to solve for x to get the major axis.

Ok, axiom has given a result -

$$\left[ {x= \%x3}, \: {x= \%x4}, \: {x={{{\sqrt {{-{{284592} \ { \%x4 \sp 2}}+{{\left( -{{189728} \ \%x3}+{{185416} \ h} -{{196504} \ c} \right)} \ \%x4} -{{284592} \ { \%x3 \sp 2}}+{{\left( {{185416} \ h} -{{196504} \ c} \right)} \ \%x3}+{{49} \ {h \sp 2}}+{{174482} \ c \ h} -{{182831} \ {c \sp 2}}}}} -{{308} \ \%x4} -{{308} \ \%x3}+{{301} \ h} -{{319} \ c}} \over {616}}}, \: {x={{-{\sqrt {{-{{284592} \ { \%x4 \sp 2}}+{{\left( -{{189728} \ \%x3}+{{185416} \ h} -{{196504} \ c} \right)} \ \%x4} -{{284592} \ { \%x3 \sp 2}}+{{\left( {{185416} \ h} -{{196504} \ c} \right)} \ \%x3}+{{49} \ {h \sp 2}}+{{174482} \ c \ h} -{{182831} \ {c \sp 2}}}}} -{{308} \ \%x4} -{{308} \ \%x3}+{{301} \ h} -{{319} \ c}} \over {616}}} \right]$$

What is this %x3?

Sounds like a substitution of x...but that's very unlikely.

I computed the result (exact result...no variables) using goal seek in openoffice...and I think it's correct.

If the length of the major axis is 100, the circumference is 200, and minor axis is 0, then the minor axis comes out to be 100...which is the right answer.

## 1. What is the major axis of an ellipse?

The major axis of an ellipse is the longest diameter of the shape, which passes through the center and connects two opposite points on the ellipse.

## 2. How is the major axis of an ellipse determined?

The major axis of an ellipse can be determined by finding the two points on the ellipse that are farthest apart and connecting them with a straight line passing through the center.

## 3. Can the major axis of an ellipse have a negative value?

No, the major axis of an ellipse cannot have a negative value. It is always measured as a positive value.

## 4. How does the major axis of an ellipse relate to its minor axis?

The major axis and minor axis of an ellipse are perpendicular to each other, with the center of the ellipse being the intersection point. The major axis is always longer than the minor axis.

## 5. What is the significance of the major axis in an ellipse?

The major axis of an ellipse is important because it represents the maximum distance between two points on the shape and is used to calculate the eccentricity and orientation of the ellipse.

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