Conic Section Formulas

If b 2 4 a c equals zero if a conic exists it will be a parabola.

Conic section formulas. Eccentricity of ellipse e c a a 2 b 2 a latus rectum of ellipse l b 2 a area of ellipse π a b. Y2 2px parametric equations of the parabola. The general equation for a conic section.

The type of section can be found from the sign. If b 2 4 a c is greater than zero if a conic exists it will be a hyperbola. Conic sections formulas parabola vertical axis horizontal axis equation x h 2 4p y k y k 2 4p x h axis of symmetry x h y k vertex h k h k focus h k p h p k directrix y k p x h p direction of opening p 0 then up.

Equations parabolas and formulas. Y mx p 2m tangent lines from a given point take a xed point p x 0 y 0. Y 0 y p x x 0 tangent line with a given slope m.

Videos related to conic sections. P 0 then down p 0 then rignt. Identify what type of conic section is given by the equation below and then find the center foci and vertices.

Standard forms of equations of conic sections. 2 parallel lines 1 line or no curve. For any of the below with a center j k instead of 0 0 replace each x term with x j and each y term.

Conic sections the parabola formulas the standard formula of a parabola 1. P 0 then left ellipse vertical major axis horizontal major axis equation 2222 22 x h y k 1 ba. The parabola is a conic section the intersection of a right circular conical surface and a plane parallel to a generating straight line of that surface.