Find a point on an ellipse given major and minor axis

sabooru

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Mar 19, 2018
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Hi I am trying to create a visual experiment in Adobe After Effects
I have an ellipse.
All values of the ellipse are available however I am unsure how to rectify them mathematically to find a point on the ellipse.

If I have the major/minor axis, starting point [0,0], horizontal ellipse

a) is it possible to find a point along the ellipse
b) is more information required to solve
c) How can I determine a coordinate where a tangent from central point would cross the ellipse?
c) i. Using either an angle input e.g. angle = theta, coordinate =?
c) ii. OR using an equation for the graphed ellipse curve from minor to major axis and using it to determinate a coordinate of a percentage distance from the starting point.

??

Can anyone help me please
Thankyou for your time considering this!
 
Hi I am trying to create a visual experiment in Adobe After Effects
I have an ellipse.
All values of the ellipse are available however I am unsure how to rectify them mathematically to find a point on the ellipse.

If I have the major/minor axis, starting point [0,0], horizontal ellipse

a) is it possible to find a point along the ellipse-yes, using the equation of the ellipse
b) is more information required to solve-the length of the major and minor axis would help
c) How can I determine a coordinate where a tangent from central point would cross the ellipse?
c) i. Using either an angle input e.g. angle = theta, coordinate =?
c) ii. OR using an equation for the graphed ellipse curve from minor to major axis and using it to determinate a coordinate of a percentage distance from the starting point.

??

Can anyone help me please
Thankyou for your time considering this!
How can both the major/minor axis be starting point at the same point,[0,0]
 
Hi I am trying to create a visual experiment in Adobe After Effects
I have an ellipse.
All values of the ellipse are available however I am unsure how to rectify them mathematically to find a point on the ellipse.

If I have the major/minor axis, starting point [0,0], horizontal ellipse

a) is it possible to find a point along the ellipse
b) is more information required to solve
c) How can I determine a coordinate where a tangent from central point would cross the ellipse?
c) i. Using either an angle input e.g. angle = theta, coordinate =?
c) ii. OR using an equation for the graphed ellipse curve from minor to major axis and using it to determinate a coordinate of a percentage distance from the starting point.

There's a lot here that I don't understand.

I can guess that what you mean by "starting point" is that the center is at the origin. Then you can easily write the equation in rectangular coordinates, or in polar coordinates if you prefer. On the other hand, if your "starting point" is a point on the ellipse, you'd have to specify where that point is relative to the vertices or whatever.

But then, what point do you want to find? What input determines it? Then, what tangent are you talking about? No tangent to the ellipse can pass through the center! And how are you measuring distance as a percentage?

Please clarify what you want, perhaps by giving a specific example.
 
The origin of the ellipse is [0,0]
I should have said the semi-minor and semi-major axis have origins of [0,0];

I think I may have solved it on my own, tell me if this is incorrect but
if the equation of an ellipse is

x2a2
+
y2b2
= 1

then I just need to select an x value on the axis, and then solve for y?
 
Hi there
Thanks for the responses and I have noticed some incorrect terminology in my OP
What I should have said was that it is a simple horizontal ellipse, with origin/centre of the ellipse being [0,0];
and should have said, semi-major axis and semi-minor axis.

x2a2
+
y2b2
= 1

I have figured out that seeing as I have both a and b values (semi major and semi minor axis)
Correct me if I'm wrong
Now I can input an x value and solve for y?

Does anyone know what the inverse of this equation would be to solve for y?
 
Is this correct in solving for y as per my responses above?

y = -(b sqrt(a^2 - x^2))/a
 
Hi there
Thanks for the responses and I have noticed some incorrect terminology in my OP
What I should have said was that it is a simple horizontal ellipse, with origin/centre of the ellipse being [0,0];
and should have said, semi-major axis and semi-minor axis.

x2a2
+
y2b2
= 1

I have figured out that seeing as I have both a and b values (semi major and semi minor axis)
Correct me if I'm wrong
Now I can input an x value and solve for y?

Does anyone know what the inverse of this equation would be to solve for y?

I believe you wanted write:

\(\displaystyle \displaystyle{\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} \ = \ 1}\)

In that case:

y = ± b * √(1 - x2/a2)

Continue.....
 
I believe you wanted write:

\(\displaystyle \displaystyle{\dfrac{x^2}{a^2} + \dfrac{y^2}{b^2} \ = \ 1}\)

In that case:

y = ± b * √(1 - x2/a2)

Continue.....

Thanks yes thats what I was trying to write but the formatting messed up. Thanks for your solution.

the solution I ended up using and have tested it is as follows:

y =± (b * (a2 - x2))/a
 
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