Geometry

Question 1

What is the general equation of midpoint of a line on the Cartesian plane?

Answer 1

Question 2

What is the general equation of a circle?

Note: trick question (Cartesian and Parametric forms)

Answer 2

Cartesian

r² = (x - a)² + (y - b)²

Where the centre has co-ordinates (a, b)

Parametric

x = a + r • cos t

y = b + r • sin t

where t is a parametric variable in the range 0 to 2π, interpreted geometrically as the angle that the ray from (a, b) to (x, y) makes with the positive x-axis.