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Distance Formula

d = square root of (x2 - x1)^2 + (y2 - y1)^2

Midpoint Formula

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

Circle definition

A circle is the set of all points in a plane that are equidistant from a fixed point.

Circle Formula

(x-h)^2 + (y-k)^2 = r^2

Parabola definition

A parabola is the set of all points in a plane equidistant from a given point and a given line.

Focus/directrix eqaution for parabola

a = (1/4p)

(find p)

(find p)

Parabola equation

opens up/down: y - k = (1 / 4p)(x - h)^2

opens left/right: x - h = (1 / 4p)(x - h)^2

p = distance from vertex to focus

opens left/right: x - h = (1 / 4p)(x - h)^2

p = distance from vertex to focus

Ellipse definition

An ellipse is the set of all point in a plane such that the sum of the distance to two fixed points is a constant.

Ellipse equation

horizontal: [(x - h)^2 / a^2] + [(y - k)^2 / b^2] = 1

Vertical: [(x - h)^2 / b^2] + [(y - k)^2 / a^2] = 1

a^2 - b^2 = c^2

Vertical: [(x - h)^2 / b^2] + [(y - k)^2 / a^2] = 1

a^2 - b^2 = c^2

Hyperbola definition

A hyperbola is the set of all points in a plane such that the difference to two fixed points is a constant.

Hyperbola equation

left/right: [(x - h)^2 / a^2] - [(y - k)^2 / b^2] = 1

Up/down: [(y - k)^2 / a^2] - [(x - h)^2 / b^2] = 1

Up/down: [(y - k)^2 / a^2] - [(x - h)^2 / b^2] = 1

1 quadratic

parabola

2 quadratics w/ same sign & same coefficient

circle

2 quadratics w/ same sign & different coefficients

ellipse

2 quadratics w/ different signs

hyperbola