Conics

A Solution to Crux Mathematicorum Problem 5109

Crux Mathematicorum Problem 5109, followed by a synthetic fixed-point argument and a projective generalization.

• Triangle geometry
• Projective geometry
• Conics

Radical Axes and Orthogonal Parabolas

Two short proofs from quadratic equations

Subtracting circle equations produces the radical axes; adding normalized equations of two parabolas with perpendicular axes produces a circle through their four intersections.

• Circles
• Conics
• Algebra