OnRamps Pre-Cal Conics

Locus Definition of a Parabola

Set of all points equidistant from a focus to a directrix

Locus Definition of a Hyperbola

Set of all points in the plane such that the absolute value of the difference of each distances from F₁ and F₂ to (x,y) is a constance distance, d

Locus Definition of an Ellipse

Set of all points in the plane such that the sum of each of the distances from F₁ and F₂ is d

Definition of a Circle

Set of points that are equidistant (radius), to a fixed point (center) in a two-dimensional plane

Identified Circle

Same number & same sign

Identified Parabola

One square (x² or y²)

Identified Ellipse

Same sign & different number

Identified Hyperbola

Different sign & same number

Horizontal Ellipse Equation

Vertical Ellipse Equation

Horizontal Hyperbola Equation

Vertical Hyperbola Equation

Vertical Parabola Equation

Horizontal Parabola Equation

Focus for an Ellipse

a² - b² = c²

Vertical Hyperbola

Negative X

Horizontal Hyperbola

Positive Y

Horizontal Ellipse

Bigger under X

Vertical Ellipse

Bigger under Y

Focus for a Hyperbola

a² + b² = c²

Eccentricity

c/a

Latus Rectum

4p