Review of Coordinate Geometry and Non-Linear Relationships

Flashcards reviewing key concepts from coordinate geometry, parabolas, hyperbolas, circles, and exponential functions, based on lecture notes.

Length, gradient, and midpoint formulas

Used to find the length, gradient, and midpoint of the interval joining two points A(x1, y1) and B(x2, y2).

Gradient-intercept form of a line

y = mx + b

Point-gradient form of a line

y - y1 = m(x - x1)

Two-point form of a line

y - y1 = (y2 - y1) / (x2 - x1) * (x - x1)

General form of a line

ax + by + c = 0, where a, b, and c are integers and a > 0

Condition for two lines to be parallel

m1 = m2

Condition for two lines to be perpendicular

m1 * m2 = -1

Median of a triangle

A line joining a vertex of a triangle to the midpoint of the opposite side.

Features of parabolas

Symmetrical about an axis of symmetry, have a vertex, and are either concave up or concave down.

General form of a parabola equation

y = ax^2

Asymptote of y=2^x for negative x

The x-axis is an asymptote for the part of the curve with negative x-values.

Asymptotes of a hyperbola

The curve approaches two lines (the x- and y-axes) but will never touch them. These lines are called asymptotes.

Equation of a circle with center (p, q) and radius r

The equation: (x - p)^2 + (y - q)^2 = r^2

Cubic curve

A curve that contains an x^3 term as its highest power.