Coordinate Geometry

Theorem 11.2 The Equation of a Circle.

The equation of a circle with its center at (a,b) and a radius r is:

r²= (x - a)² + (y - b)²

Slope of a line:

Theorem:

If the slope of two lines are equal then the line are parallel.

Theorem:

If the product of the slopes of two non-vertical lines is -1 then the
lines are perpendicular.

Theorem: The Standard Equation of a Line.

Any equation that can be written as ax + by = c, where a and b are
nonzero numbers, is a line.

Theorem: Point-Slope Form

The equation of a line with point  and slope m is:

y -y1 = m(x - x1)

Theorem: The Slope-Intercept Form

The equation of a line with slope m and y-intercept b is:

y = mx + b