MTH 209 Exam 1 Formulas

Standard Form of a Parabola (Vertical Axis)

Standard Form of a Parabola (Horizontal Axis)

Coordinates of focus (vertical axis)

Coordinates of focus (horizontal axis)

Standard Form of an Ellipse (Horizontal Major Axis)

Standard Form of an Ellipse (Vertical Major Axis)

foci (ellipse)

eccentricity of an ellipse and a hyperbola

Standard Form of a Hyperbola (Horizontal Transverse Axis)

Standard Form of a Hyperbola (Vertical Transverse Axis)

Vertices and Foci of Hyperbola

Hyperbola Asymptote (Horizontal Transverse Axis)

Hyperbola Asymptote (Vertical Transverse Axis)

Parametric Form of the Derivative

Arc Length in Parametric Form

Area of a Surface of Revolution (Revolution about the x-axis, g(t) > or equal to 0)

Area of a Surface of Revolution (Revolution about the y-axis, f(t) > or equal to 0)

Polar to Rectangular Conversion

Rectangular to Polar Conversion

Slope in Polar Form

Rose curve

Limacon

Circle

Lemniscate

Area in Polar Coordinates

Arc Length of a Polar Curve

Area of Surface of Revolution (About the Polar Axis)

Area of Surface of Revolution (About the line θ =  π/2)

Polar Equation of Conic (Horizontal directrix above the pole)

Polar Equation of Conic (Horizontal directrix below the pole)

Polar Equation of Conic (Vertical directrix to the right of the pole)

Polar Equation of Conic (Vertical directrix to the left of the pole)

Length/Magnitude of a Vector

Vector sum (Vector Addition)

Scalar Multiplication

Length of a Scalar Multiple

Unit Vector in the Direction of v

linear combination of i and j