Conic

[lrp]

How do I get the eccentricity, latus rectum, loci, etc of a conic . Also the directrix of a parabola without having to graph it.

[sxk1693]

Eccentricity of a conic is: [unparseable or potentially dangerous latex formula]

If you don't know what c or a is, then just ask.

[Fredfredburger]

Hmm, let's see.

First of all a locus is a collection of points that satisfy a distinct property, not a numerical derivation.

For a circle, defined as a locus of points equidistant from a fixed center, in standard form with center (h,k) and radius r,
[unparseable or potentially dangerous latex formula]
Eccentricity: [unparseable or potentially dangerous latex formula]
Latus Rectum: [unparseable or potentially dangerous latex formula]

For an ellipse, defined as a locus of points such that the sum of the the distance between the points and the two foci is constant, and equivalent to the major axis, in standard form with center (h,k),
[unparseable or potentially dangerous latex formula]
Major Axis, Minor axis:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

Foci:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
where
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

Eccentricity:
[unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula] or [unparseable or potentially dangerous latex formula]

Latus rectum:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

Directrix:
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]

That took a long time, so I'll only do the ones on one axis, you could piece together the rest...

For a parabola, defined as a locus of points equidistant from the directrix and the focus, in standard form with vertex (h,k),
[unparseable or potentially dangerous latex formula]
Eccentricity: [unparseable or potentially dangerous latex formula]

Latus Rectum: [unparseable or potentially dangerous latex formula]

Focus: [unparseable or potentially dangerous latex formula]

Directix: [unparseable or potentially dangerous latex formula]

Now for a parabola in the form
[unparseable or potentially dangerous latex formula]

Axis of symmetry:
[unparseable or potentially dangerous latex formula]

Focus:
[unparseable or potentially dangerous latex formula]

Directrix:
[unparseable or potentially dangerous latex formula]

Latus Rectum:
[unparseable or potentially dangerous latex formula]

For a hyperbola, defined as a locus of points such that the absolute value of the difference from the two foci is a constant, namely the major axis, 2a, in standard form centered around (h,k),
[unparseable or potentially dangerous latex formula]

Foci:
[unparseable or potentially dangerous latex formula]

Directixes:
[unparseable or potentially dangerous latex formula]

Eccentricity:
[unparseable or potentially dangerous latex formula]

Latus Rectum:
[unparseable or potentially dangerous latex formula]

Asymptotes:
[unparseable or potentially dangerous latex formula]

Also read up on the double-napped cone definitions for conics, and maybe polar representations of them, that's the only other stuff I can think of that might pop up.

[sxk1693]

Wow, how long did it take you to type all that?

That is a good explanation though... I would have told aeroman to just look it up on that super secret website that you, Fredburger, told me to go to.

[lrp]

Which is what website ? If i could ask.

[darksaber21]

[007math]

[darksaber21]

That is true, that is true.

[Calculus98]

Also to find the directrix of a parabola you can find the equation in standard form, solve for a, then subtract it from the y term of the vertex if is a vertical parabola, or subtract it from the x term of the vertex if it is a horizontal parabola.

[sxk1693]

Actually the super secret website is: this: [url]wikipedia.com[/url]