The focus triangle of an ellipse is a triangle formed by the two foci of an ellipse and any point on the ellipse as the three vertices of the triangle, i.e. the two vertices are the focus of the ellipse and the other vertex is on the ellipse.

The formula for the area of the focal triangle of an ellipse is S = b^2 * tan(θ/2), where b is the length of the minor axis of the ellipse, θ is the angle of eccentricity of the ellipse, and the minor axis is the shortest diameter of the ellipse. Although elliptic focal triangles have few applications in life, they are of great importance in the study of mathematics and geometry and can help us to understand the properties and characteristics of ellipses more deeply. Below is a proof of the formula for the area of elliptical triangles:

An elliptic focal triangle is a special type of triangle whose vertices are the two foci and one point of the ellipse. It has some special properties, such as the fact that the sum of the lengths of its three sides is equal to the circumference of the ellipse, and the fact that its centre is the centre of the ellipse. Although elliptic focal triangles have fewer applications in life, they are of great importance in the study of mathematics and geometry and can help us to understand the properties and characteristics of ellipses more deeply.

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