Ellipse

An ellipse is a set of points in the plane, where the sum of the distances of the points from two fixed points is constant. The two points are called focal points.

Ellipse

$r_{1} + r_{2} = 2 a = c o n s t$

$e = \sqrt{a^{2} - b^{2}}$

Ellipse

\frac{(x - u)^{2}}{a^{2}} + \frac{(y - v)^{2}}{b^{2}} = 1

Central Ellipse

\frac{x^{2}}{a^{2}} + \frac{y^{2}}{b^{2}} = 1

Focal points of a Central Ellipse

Horizontal ellipse (a>b):

a > b \to F_{1} (- e, 0); F_{2} (e, 0); e = \sqrt{a^{2} - b^{2}}

Vertical ellipse (a<b):

$a < b \to F_{1} (0, e); F_{2} (0, - e); e = \sqrt{b^{2} - a^{2}}$

Tangency condition of a central ellipse and a line

a^{2} \cdot k^{2} + b^{2} = n^{2}

where the equation of the tangent line is :

y = k x + n

Keywords: ellipse, central ellipse, equation of an ellipse, tangent to a ellipse

Trigonometry
Law of Sines
Law of Cosines
Trigonometric identities of double angles
Trygonometry Identities of same angle
Trigonometric identities of half angles
Identities for the sum and difference of two angles
Sum and difference of trigonometric functions
Trigonometric Values of Special Angles
Two-dimensional geometric shapes
Angle Bisector Theorem
Basic Proportionality Theorem - Intercept Theorem
The inscribed angle theorem
Convex - Concave polygons, functions
Triangle
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Quadrilateral
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Analytical Geometry 2D
Distance between two points
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Ellipse
Analytical Geometry 3D
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