Pre-Calculus: Cheats for Answering Conic Section Problems

K to 12 Senior High School
Pre-Calculus

Cheats for Answering Conic Section Problems

Answering Mathematics problems is undeniably tricky. However, you can be ahead of others during exams if you use the cheats I will give to you down below. But don't worry. These cheats aren't actually cheats but are just useful formula for answering problems related to conic sections. So, let's get into it.

CIRCLE

   Standard Form: (x-h)^2 + (y-k)^2 = r^2
   General Form: x^2 + y^2 + Cx + Dy + E = 0
   Center: (h, k)
   Radius: r
   Points: (h, k+r), (h, k-r), (h+r, k), (h-r, K)

ELLIPSE

   Standard Form: [(x-h)^2 ]/a^2 + [(y-k)^2]/b^2 = 1
   General Form:
   Center: (h, k)
   c = square root of a^2 - b^2
         (the table below are the formula for both vertical and horizontal ellipse)
Major Axis Horizontal         Vertical
Foci         (h+c, k) and (h-c, k) (h, k+c) and (h, k-c)
Vertices         (h+a, k) and (h-a, k) (h, k+a) and (h, k-a)
Co-vertices (h, k+b) and (h, k-b) (h+b, k) and (h-b, k)

[NOTE: >The longer axis is the major axis
> a^2 is the larger between the 2 denominators
> c is the distance from the center to the foci
> Foci are always found along the major axis ]

HYPERBOLA

   Standard Form: [(x-h)^2 ]/a^2 - [(y-k)^2]/b^2 = 1
   Center: (h, k)
         (the table below are the formula for hyperbola with horizontal or vertical transverse axis)
Transverse Axis Horizontal             Vertical
Foci           (h+c, k) and (h-c, k)     (h, k+c) and (h, k-c)
Vertices         (h+a, k) and (h-a, K)     (h, k+a) and (h, k-a)
Asymptotes y = (+/-) (b/a) (x-h) +k     y = (+/-) (a/b) (x-h) +k

[NOTE: > a^2 is always positive and comes first in the equation]

PARABOLA

   General Form: Ax^2 + Cx + Dy + E = 0
  By^2 + Dy + Cx + E = 0

Vertex at Origin Focus Directrix         Opening of Graph
y^2 = -4cx (-c, 0) x = -c Left
y^2 = 4cx (c, 0) x = c Right
x^2 = 4cy (0, c) y = c Downward
x^2 = -4cy (0, -c) y = -c Upward



Vertex at (h, k) Focus Directrix         Opening of Axis of
                        Graph Symmetry
(y-k)^2 = -4c(x-h) (h-c, k) x=h+c Left          y=k
(y-k)^2 = 4c(x-h)    (h+c, k) x=h-c Right y=k
(x-h)^2 = 4c(y-k) (h, k+c) y=k-c Upward    x=h
(x-h)^2 = -4c(y-k) (h, k-c) y=k+c Downward x=h

                           Memorizing, understanding, and practicing how to use the formula will give you a sure ace during exam. You can definitely finish it in no time and reserve your energy for other important matters. This should help. :)

                           Thank you!