## Parabolas with vertex (h,k)
Any point on a parabola is equidistant from the parabola's focus and directrix ## Conic Cross-Sections Diagram## Parabola opening upwards |
## Circles/Ellipses with center (h,k)
c²=a²-b² and |a|≥|b|>0 Formulas for foci generate two different points (+c and -c), and formulas for vertices generate four different vertices: (h+a,k) (h-a,k) (h,k+b) and (h,k-b) Distances between a focal point to any point on the ellipse, plus the distance of the other focal point to that same point on the ellipse, gives a sum of distances that is constant for any point on the ellipse ## Wide Ellipse |
## Hyperbolas with center (h,k)
c²=a²+b², |a|≠0, |b|≠0 Formulas for foci generate two different points (+c and -c), formulas for vertices generate two different points (+a and -a), and formulas for asymptotes generate two different asymptotes (+(a/b) and -(a/b) or +(b/a) and -(b/a)) Distance of a focal point to a point on either hyperbola branch, minus distance of the other focal point to that same point on that same hyperbola branch, gives a value whose magnitude is constant for any point on either hyperbola branch ## Horizontal pair of Hyperbolas## Horizontal Hyperbola Asymptotes |

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# 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

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