Sign up
|
Login
Home
|
Math
|
Physics
|
Chemistry
|
Other
|
Tools
Submit New Formulas/Articles
Recently Added Math Formulas
·
Polynomials Second Degree
·
Polynomials Basic
·
Logarithmic Identities
·
Exponential Functions
·
Powers
Additional Formulas
·
Closure Property - Multiplication
·
Properties of Equality
·
Closure Property Addition
·
Logarithmic Identities
·
Exponential Functions
|
More
Math Formulas
>
Algebra
> Conic Section
Conic Section
By intersecting a cone with a plane, a curve is obtained and is named conic section, which is the red area shown above.
The expression for a conic section in the Cartesian coordinate system is defined as:
A
x
2
+ B
xy
+ C
y
2
+ D
x
+ E
y
+ F = 0
A ≠ 0, B ≠ 0 and C ≠ 0
The result of B
2
– 4AC determines the type of the conic section obtained:
• If the result is smaller than 0, then we have an ellipse, unless the conic is degenerate.
o The ellipse is defined as:
x
2
/a
2
+
y
2
/b
2
= 1 and
x
2
/b
2
+
y
2
/a
2
= 1
• If the result is smaller than 0 and A=C, B=0 then we have a perfect circle.
o The circle is defined as:
x
2
+
y
2
= r
2
• If the result is equal to 0, then we have a parabola.
o The parabola is defined as:
y
2
= 4 ∙ a ∙
x
and
x
2
= 4 ∙ a ∙
y
• If the result is bigger than 0, then we have a hyperbola.
o The hyperbola is defined as:
x
2
/a
2
–
y
2
/b
2
= 1 and
y
2
/a
2
–
x
2
/b
2
= 1
• If the result is bigger than 0 and A+C = 0, then we have a rectangular hyperbola.
o The rectangular hyperbola is defined as:
x
∙
y
= c
2
Amazon.com Widgets
Leave a Comment:
Contact us
|
Terms of Use
|
Privacy Policy
| Web-Formulas.com © 2008 -
2010
