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(x - a)² + (y - b)² = r²

Circle

m1 = m2

Parallel Lines

y - y1 = m(x - x1)

Staight Line

m1 x m2 = -1

Perpendicular Lines

b² - 4ac > 0

2 Real Roots

b² - 4ac = 0

Repeated Root

b² - 4ac < 0

No Real Roots

y = f(x) + a

Translate by a units parallel to y-axis

y = f(x - a)

Translate by a units parallel to x-axis

y = af(x)

Stretch parallel to y-axis by scale factor a

y = f(ax)

Stretch parallel to x-axis by scale factor 1/a

(x2 - x1)² + (y2 - y1)² = AB²

Length of a Line

(y2 - y1) / (x2 - x1)

Gradient of a Line

([x1 + x2] / 2 , [y1 + y2] / 2)

Midpoint of a Line

dy/dx = 0

Stationary Point

d²y/dx² > 0

Local Min

d²y/dx² < 0

Local Max

Perpendicular Gradient

Negative Recipricol of gradient

( -b , c )

Minimum Point of a(x + b)² + c

dy/dx > 0

Increasing Function

dy/dx < 0

Decreasing Function

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