An arbitrary point B on the unit circle is reflected in the y-axis to give B’. D is the intersection of BC and AB’. Prove it lies on the red hyperbola.

Puzzle creator: Matthew Arcus.

Scroll down for a solution to this problem.

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- Post author By Rik D. Tangerman
- Post date October 20, 2023
- 2 Comments on A hyperbolic style

An arbitrary point B on the unit circle is reflected in the y-axis to give B’. D is the intersection of BC and AB’. Prove it lies on the red hyperbola.

Puzzle creator: Matthew Arcus.

Scroll down for a solution to this problem.

## 2 replies on “A hyperbolic style”

Here’s a neat way to derive the equation of the hyperbola:

This is with C as centre and the x-axis going out to the left.