Angle between tangents to an inner and outer concentric similar ellipse

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If we examine the two tangents to an inner conic which pass through a point on the outer conic, we see that each makes the same angle with the outer conic.

Further we see that the triangle formed by the three points of contact has an area which is independent of the location of the outer point (parameter t).

Expressions

Name Input
Area Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Angle 1 Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image
Angle 2 Derive Input Maple Input MathML Input Mathematica Input Maxima Input Mupad Input TI-Nspire Input text Input Image