Anonymous
Anonymous asked in Science & MathematicsMathematics · 2 months ago

# What are the relationships between circle, ellipse, parabola and hyperbola?

Relevance
• 2 months ago

They are all 'conic' sections.

• 2 months ago
• david
Lv 7
2 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.