Jean Miles: Conic Sections, equations, SoE

shrimpeh: hey jean, can I haz help again?
Jean: ehh, fine. This worked for you before, so...
shrimpeh: yayyy ^^

Hi again, I'm Jean, your friendly Uprising VP, here to help shrmpeh with more math because he sucks at it. Alright, I'll start now.

Conic Sections in General
Conic sections are basically the different shapes you would find if you cut a cone up into different sections. Depending on where and the angle that you cut the shape, it will create a different section.

There are 4 different conic sections:

1) Circle
2) Ellipse
3) Parablola
4) Hyperbola

Circle

A circle's equations are:
x² + y² = r²
(x-h)² + (y-k)² = r²

Circles have an x2, a y2 and the same coefficients. It has not been scaled in any way.

Ellipse

An ellipse's equations are:
ax² + by² = c
x²/a + y²/b = 1
a does not equal b (the coefficients are different)

Parabola

A parabola's equations are:

y = ax² + bx + c

Hyperbola

A Hyperbola has 3 equations:

xy = k (inverse variation parabola)
ax² - by² = c
ay² - bx² = c

Once you have figured out what a conic section is, a good idea is to solve it in order to see what transformation has occurred.

Some ways to solve this is simply getting y by itself (parabola)
But mainly, you must reduce it to an equation by using formulas such as:

completing the square
getting y by itself

Systems of Equations
For this chapter, you'll have to solve system for equations for circles, parabolas, hyperbolas and ellipses. It is important to know which formulas can solve this:

1) Graphing. However, this is not always a good idea for the points of interception (which is what you solve for) is not always on the graph, and sometimes is a rather messy number

2) Elimination
2) Substitution