Ellipse centered in focis with axis inclination

[kepler]

Greetings

I'm trying to determine the equation of an ellipse with center in one focis, and the major axis with an inclination.
The equation of a ellipse centered in the focis is given, I believe, by:

(x-c)²/a² + y²/b² = 1 where the focis coordinates are (c,0)

So

y² = 1 - (x-c)²/a²

but supose the major axis is inclined by 30 degrees, and the center is all ways the focis? Y² will be equal to what?
Rotating coordinates is easy. Still, I'm not sure of the final equation solved to y.

Thanks in advance.

Kind regards

Kepler

 

[stapel]

I'm trying to determine the equation of an ellipse with center in one focis...

I'm not sure what you mean by this...? If the center is at a focal point, isn't the ellipse actually a circle?

...and the major axis with an inclination. The equation of a ellipse centered in the focis is given, I believe, by:

(x-c)²/a² + y²/b² = 1 where the focis coordinates are (c,0)

So y² = 1 - (x-c)²/a²

but supose the major axis is inclined by 30 degrees, and the center is all ways the focis? Y² will be equal to what?
Rotating coordinates is easy. Still, I'm not sure of the final equation solved to y.

It sounds like rotation of axes is exactly what you need to do. But, for us to be able to check your work ("the final equation..."), we'll need to see it first. Please reply with that information. Thank you!

 

[kepler]

I'm not sure what you mean by this...? If the center is at a focal point, isn't the ellipse actually a circle?


It sounds like rotation of axes is exactly what you need to do. But, for us to be able to check your work ("the final equation..."), we'll need to see it first. Please reply with that information. Thank you!

Good morning

Thanks for the help. I'm trying to generalize thye problem. But let's say I have an ellipse with center at (-2,-2), and one of the focis at (0,0); the focis will have a length of 2*(2^0.5). One of the point - the nearest of the focis - is (1,1) - thus the a semi axis is 2^0.5+2*(2^0.5) = 3*(2^0.5)

What is the y equation?

Kind regards

Kepler