06-02-2013, 04:21 PM
Coordinate geometry in the (x, y)-plane
Coordinate geometry.pdf (Size: 89.32 KB / Downloads: 138)
Special cases
The line through (1, 1) and (3, 1) has gradient (1−1)/(3−1) = 0, that is, it is horizontal.
It has equation y = 0x + 1, that is, y = 1.
The line through (3, 1) and (3, 6) has gradient (6 − 1)/(3 − 3) = 1, that is, it is vertical.
Vertical lines cannot be written in the form y = mx + c, but rather in the form x =
constant. Here the equation is x = 3.
Parametric equations.
The curve is given by two equations, x = f(t) and y = g(t),
for suitable functions f(t) and g(t). These give the coordinates of any point of the curve
in terms of a new independent variable, t, called the parameter.
To plot the curve, calculate f(t) and g(t) for a range of values of t, and plot the corre- sponding points