Where is $\theta$ measured from in an ellipse?

Question

A general point in a an ellipse is given by $(A \cos \theta, B \sin \theta)$.

Where is this $\theta$ measured from? Is it between the point and origin or the angle made by the normal at that point and the $x$-axis?

https://en.wikipedia.org/wiki/Ellipse#Parametric_representation — amd, Mar 15 '19 at 19:59

score 1 · Accepted Answer · answered Mar 15 '19 at 16:00

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GEOMETRIC INTERPRETATION OF THE PARAMETER $\theta$ IN THE EQUATION $(acos\theta,bsin\theta)$ OF THE ELLPISE:-

It is the polar angle of corresponding point(that is the closest point sharing the same x coordinate)on auxiliary circle(circle with major axis of ellipse as diameter and center as centre of ellipse) of a point in an ellipse,in the coordinate system with origin in the centre of the ellipse.

answered Mar 15 '19 at 16:00

Bijayan Ray

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perfect! the answer i was looking for. – Lelouche Lamperouge Mar 15 '19 at 16:05

score 1 · Answer 2 · answered Mar 15 '19 at 16:23

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Radial rays inclined at angle $\theta$ to x-axis cut two concentric circles.

Lines parallel to $(x,y)$ axes through above intersections points again cut at each parameterized point of an ellipse.

Image copied from internet mysite.du.edu

answered Mar 15 '19 at 16:23

Narasimham

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score 0 · Answer 3 · answered Mar 15 '19 at 15:49

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$\theta$ in this parameterization is not an angle that can be measured anywhere in the ellipse itself.

It is an angle in the circle you squish from the sides to make the ellipse, but that has no immediate interpretation as a geometric angle in the final result.

answered Mar 15 '19 at 15:49

hmakholm left over Monica

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ok that explains everything. thanks – Lelouche Lamperouge Mar 15 '19 at 15:52

Where is $\theta$ measured from in an ellipse?

3 Answers3