Maths WorkshopMaths problems with full solutions

Analytic geometry

8 problems · Cartesian coordinates, lines, conic sections and parametric curves.

Ex.181Area from coordinates
#vectors #area
Analytic geometry
High school
High school
Ex.324Distance from a point to a line
#lines #projection
Analytic geometry
High school
High school
Ex.641Two classical locus problems
#locus #coordinates #perpendicular #circle with a given diameter
Analytic geometry
M1
M1
Ex.1315Equilateral triangles and complex numbers
#complex numbers #equilateral triangle #roots of unity #rotation
Analytic geometry
Olympiad
Olympiad
Ex.1317Pick's theorem and lattice triangles
#Pick's theorem #lattice points #area #equilateral triangle
Analytic geometry
Olympiad
Olympiad
Ex.1318The Apollonius circle
#locus #Apollonius circle #coordinates #angle bisector
Analytic geometry
Olympiad
Olympiad
Ex.1319The distance between the circumcentre and the orthocentre
#vectors #orthocentre #circumcentre #Euler line
Analytic geometry
Olympiad
Olympiad
Ex.1987The butterfly theorem
#butterfly theorem #chords #coordinates #Vieta
Analytic geometry
Olympiad
Olympiad