Math Formulas: Conic Sections

The Parabola

Parametric equations of the parabola:

Tangent line in a point D(x₀,y₀) of a parabola y² = 2px :

Tangent line with a given slope (m):

Tangent lines from a given point

Take a fixed point P(x₀,y₀). The equations of the tangent lines are:

The Ellipse

The set of all points in the plane, the sum of whose distances from two fixed points, called the foci, is a constant.

The standard formula of a ellipse:

Parametric equations of the ellipse:

Tangent line in a point D(x₀,y₀) of a ellipse:

Eccentricity:

Foci:

Area:

The Hyperbola

The set of all points in the plane, the difference of whose distances from two fixed points, called the foci, remains constant.

the standard formula of a hyperbola:

Parametric equations of the Hyperbola:

Tangent line in a point D(x₀,y₀) of a Hyperbola:

Foci:

Asymptotes: