Cheatography

# Conic Sections Cheat Sheet by CROSSANT

Graphics sourced from these websites: Conic Cross-Sections https://www.ck12.org/book/ck-12-algebra-ii-with-trigonometry-concepts/section/10.0/ Labelled Parabola, Ellipse, and Hyperbola https://math.libretexts.org/Bookshelves/Calculus/Calculus_3e_%28Apex%29/09%3A_Curves_in_the_Plane/9.01%3A_Conic_Sections

### Parabolas with vertex (h,k)

 Opening up/down (x-h)2=±4p(y-k) Focus (h+p, k) Directrix y=k-p Opening right/left (x-h)=­±4p­(y-k)2 Focus (h,k+p) Directrix x=h-p

### Ellipses with center (h,k)

 Circle (x-h)2+(y-k)2=r2 Focus=­Center (h,k) Vertices None Wide Ellipse (x-h)2/a2+(y-k)2/b2=1 Foci (h±c, k) Vertices (h±a, k±b) Tall Ellipse (x-h)2/b2+(y-k)2/a2=1 Foci (h, k±c) Vertices (h±b, k±a)
a≥b>0 and c²=a²-b²

### Hyperbolas with center (h,k)

 Pair opening left and right (x-h)2/a2-(y-k)2/b2=1 Foci (h±c, k) Vertices (h±a, k) Asymptotes y-k=±(­b/a­)(x-h) Pair opening up and down (y-k)2/a2-(x-h)2/b2(=1 Foci (h, k±c) Vertices (h, k±a) Asymptotes y-k=±(­a/b­)(x-h)
c²=a²+b²