What are the relationships between circle, ellipse, parabola and hyperbola?
- lenpol7Lv 72 months ago
They are all 'conic' sections.
- davidLv 72 months ago
The greeks called them conic sections. They can be created by slicing thru a cone (actually a double cone) in different directions.
cut parallel to the base and you get a circle
imagine a plane tangent to the conealong the outer side of it .. move over just a little and this cuts thru the cone making a parabola
... the double cone has 2 parallel bases (both are circles) ..imagine a line from the center of one base to the other. Again move parallel to that line .. this will cut thru bothe the top and bottom cones creating the hyperbola ==
next cut thru the cone not parallel to the base and not parallel to the tangent plane .. just some odd angle -- this will create an ellipse.
..... All these can be generalized with algebraic equations
Ax^2 + Bx + Cy^2 +Dy + Exy + F = 0
by changing the values of A, B, C, D, E and F you get those 4 conic sections ---- Sor example --- simple circles can be created when A = C and E is 0 ... other changes will create the other conics.