Coordinate Geometry & the Circle

Coordinate geometry turns geometry into algebra.

Straight lines

Gradient $m = \dfrac{y_2 - y_1}{x_2 - x_1}$; equation $y - y_1 = m(x - x_1)$.
Parallel lines have equal gradients; perpendicular gradients multiply to $-1$.
Distance $= \sqrt{(x_2 - x_1)^2 + (y_2 - y_1)^2}$; midpoint $= \left(\tfrac{x_1+x_2}{2}, \tfrac{y_1+y_2}{2}\right)$.