parabolas, circles, and ellipses

general equation of parabolas

ax² + bxy + cy² + dx + ey +f = 0

standard form

(x-h)² = 4p(y-k)

standard form

(y-k)² = 4p(x-h)

standard equation of parabola with vertex at origin

x² = 4py

y² = 4px

what to do with vertex and directrix

find p using p = k/h - directrix

what to do when given focus and directrix

add directrix with matching x or y and divied by 2 to get h or k

standard form of circle

(x-h)² + (y-k)² = r²

radius formula

root x -x1 squared + y - y1 squared

how to find circle with end points

mid point formula add both x and divide by 2

ellipse

set of points such that the distance between that point and two fixed points called foci remaisn constant

major axis

line through foci

center

midpoint of major axis

verticies

intersection of major axis

a

center to vertex

b

center to co vertex

c

distance from center to focus

c² =

a² - b²

horizontal major axis

x-h²/a² + y-k²/b² = 1

vertical major axis

x-h²/b² + y-k²/a² =1

eccentricity

e = c/a