# What is the general equation of the ellipse that is not in the origin and rotated by an angle?

I have the equation not in the center, i.e.

$$\frac{(x-h)^2}{a^2}+\frac{(y-k)^2}{b^2}=1.$$

But what will be the equation once it is rotated?

## Answer

After a lot of mistakes I finally got the correct equation for my problem:-

$$\dfrac {((x-h)\cos(A)+(y-k)\sin(A))^2}{a^2}+\dfrac{((x-h) \sin(A)-(y-k) \cos(A))^2}{b^2}=1,$$

where $$h, k$$ and $$a, b$$ are the shifts and semi-axis in the $$x$$ and $$y$$ directions respectively and $$A$$ is the angle measured from $$x$$ axis.

Attribution
Source : Link , Question Author : andikat dennis , Answer Author :
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