What is the general equation of ellipse?

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Solution

General Equation of Ellipse:
An ellipse is one of the types of conic sections.
If a plane cut a cone with an angle with $x$ -axis.
Then closed $2$ dimensional shape (ellipse) is formed.
The general equation of an ellipse is $\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1$ .
The center of the ellipse is $(0, 0)$
The coordinate of the vertices are $(\pm a, 0)$ .
The coordinate of the covertices are $(0, \pm b)$ .
The eccentricity of the ellipse is $e = \sqrt{1 - \frac{b^{2}}{a^{2}}}$
The coordinate of foci are $(\pm a e, 0)$ .
The directrices of the ellipse are $x = \pm \frac{a}{e}$

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