An ellipse with its focal points, major and minor axis. What is x, the distance from the centre to the right focal point?
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Egg of Columbus
Tag: ellipse
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A good egg
An ellipse with its focal points and a tangent line. What is the angle α?
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Pumpkin tracing
The point E moves along the outer circle whose center is G. Points A and B are fixed, whereas F and B’ vary with E. Show that F traces an ellipse as E moves along the outer circle.
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The gondola lift
A tangent and its normal in an arbitrary point on an ellipse with eccentricity e. The focal points are also shown. What is the minimum value of blue : red in terms of e?
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Ellipsoidal laser
The inside surface of an ellipse is a perfect mirror. There is a pin-hole at an end of the diameter. Show that a light ray emitted from either focus will exit the enclosure via the pin-hole, perhaps after bouncing through the foci several times.
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The lorgnette
An ellipse, two circles centred in its focal points, a chord and a tangent. What is the angle α?
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Pushing the boundary
Two equilateral triangles are placed side by side. What’s the proportion green : red?
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The gyroscope
Two ellipses go through each others focal points. Prove that the focal points are the vertices of a parallelogram.
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The Pappus eggs
Three semicircles and a circle with their centres. Two orange ellipses with focal points in the semicircle centres (they share the middle one). Prove that their upper intersection point coincides with the circle centre.
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The sliding ladder
A ladder seen from the side is sliding down a wall. Prove that a fixed point on the ladder traces part of an ellipse.