How would I be able to find the width of a horizontal ellipse (with a major axis of 120 and a minor axis of 5) at any given point along the major axis?
[Math] How to find the width of a given section of an ellipse
conic sectionsgeometry
conic sectionsgeometry
How would I be able to find the width of a horizontal ellipse (with a major axis of 120 and a minor axis of 5) at any given point along the major axis?
Best Answer
To solve your question you just need to write the equation of the ellipse. The most natural coordinates for writing the equation are the ones where the origin coincides with the center of the ellipse and the major and minor axes are along the $x$ and $y$-axes respectively. In this coordinate system, the equation of your ellipse is $x^2/(60)^2+y^2/(2.5)^2=1$. Now given a point $(a,0)$ on the major axis, all you need to do is find the values of $y$ which satisfy the equation $a^2/(60)^2+y^2/(2.5)^2=1$. The difference of these values of $y$ is the width of the ellipse at $(a,0)$. Can you see why?