Conic Section Formula Sheet

Here h k 0.

Conic section formula sheet. The type of conic represented by the general equation of the second degree in two variables. The standard formula of a ellipse. Simple technique to recognise different conic sections.

X2 a2 y2. 4𝑐𝑐 𝑦𝑦 𝑘𝑘 𝑦𝑦 𝑘𝑘 2 4𝑐𝑐 𝑥𝑥 ℎ axis of symmetry 𝑥𝑥 ℎ 𝑦𝑦 𝑘𝑘 focus ℎ 𝑘𝑘 𝑐𝑐 ℎ 𝑐𝑐 𝑘𝑘 directrix 𝑦𝑦 𝑘𝑘 𝑐𝑐 𝑥𝑥 ℎ 𝑐𝑐 opening upward if 𝑐𝑐 0 downward if 𝑐𝑐 0 right if 𝑐𝑐 0 left if 𝑐𝑐 0. 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.

Find an equation of the circle with centre at 0 0 and radius r. The set of all points in the plane the sum of whose distances from two xed points called the foci is a constant. Circle conic section when working with circle conic sections we can derive the equation of a circle by using coordinates and the distance formula.

If α β the conic section formed is a parabola represented by the orange curve as shown below. A conic section can be graphed on a coordinate plane. P 0 then down p 0 then rignt.

Ax 2 2bxy cy 2 2dx 2ey f 0. If α β 90 o the conic section so formed is an ellipse as shown in the figure below. Therefore the equation of the circle is x 2 y 2 r 2.

The general equation for any conic section is a x 2 b x y c y 2 d x e y f 0 where a b c d e and f are constants. Frac 2b 2 a conic section formulas examples. A conic section or simply conic is a curve obtained as the intersection of the surface of a cone with a plane.