Information about Focus and Region

[jean05]

Information about Locus and Region

Hi
I need to study about Locus defined by an equality and region defined by inequalities, i found the concept of locus and i undertand it, but i dont find a good website to learn about it. If someone can tell me a short explanation or a good website to learn about it, i really appreciate that
Also, i find that region is the zone that satisfies the inequality when you graph it, i dont know if it is something like that or am i wrong?
Thanks for your time (sorry if i wrote something wrong)

 

[HallsofIvy]

I have several problems understanding this. First, in you title you have "focus" but in the body "locus". I assume you mean "locus" in both places. A "locus" is a set of points satisfying some condition. If a locus is given by a single equation, then it is the set or points satisfying that equation- the graph of the equation.

"I find that region is the region satisfying these inequalities when you graph it, i dont know if it is something like that or am i wrong?"

The word "region" just means a set of points though it implies a two dimensional set of points (as opposed to a line or curve) in the plane. There has to be some condition put on the region in order for you to find it. If the problem says "Find the region satisfying these inequalities" then, obviously, yes, it is "the region satisfying these inequalities"! The simplest way to do this is to first graph the corresponding equations (replace "<" or ">" with "=") since those form the boundaries, then which side of that line or curve satisfies the inequality and which does not.

 

[jean05]

I have several problems understanding this. First, in you title you have "focus" but in the body "locus". I assume you mean "locus" in both places. A "locus" is a set of points satisfying some condition. If a locus is given by a single equation, then it is the set or points satisfying that equation- the graph of the equation.

"I find that region is the region satisfying these inequalities when you graph it, i dont know if it is something like that or am i wrong?"

The word "region" just means a set of points though it implies a two dimensional set of points (as opposed to a line or curve) in the plane. There has to be some condition put on the region in order for you to find it. If the problem says "Find the region satisfying these inequalities" then, obviously, yes, it is "the region satisfying these inequalities"! The simplest way to do this is to first graph the corresponding equations (replace "<" or ">" with "=") since those form the boundaries, then which side of that line or curve satisfies the inequality and which does not.

sorry about that, yestertay i was really tired.
that is what i find about locus, but i dont know what kind if problems i need to do with it? if is only the graph of the equation is easy but i dont think thats all.
This is the syllabus from where im studying :

you dont know a website where i can study about this?

 

[Otis]

if [locus] is only the graph of the equation is easy but i dont think thats all.

That's all, for the locus of equations.

As HallsofIvy said, "locus" is another name for "the set of solutions". Equations of lines and circles have infinite solutions because lines and circles are composed of infinite points. We can't list them all, so we draw a graph, instead, to show all the solutions (locus).

The section (2) "Locus and Regions" is talking about graphing.

So for you in this course, a locus will almost always be a graph of an equation containing x and y (it will be either a line or a circle, depending on the equation).

And, in this course, a region will almost always be a graph of an inequality containing x and y (it's either the region above or below a line or the region inside or outside a circle, depending on the inequality).

In other words, a region is a locus where all of the (x,y) solution points form an area, instead of a line or circle.

You can start learning about graphing linear inequalities in x and y (regions above or below a line) by googling graphing linear inequalities in two variables. You will find video lectures (like Khan Academy) or written lessons (like PurpleMath).

If you need help with something you see, please start a new thread. Cheers

 

[jean05]

That's all, for the locus of equations.

As HallsofIvy said, "locus" is another name for "the set of solutions". Equations of lines and circles have infinite solutions because lines and circles are composed of infinite points. We can't list them all, so we draw a graph, instead, to show all the solutions (locus).

The section (2) "Locus and Regions" is talking about graphing.

So for you in this course, a locus will almost always be a graph of an equation containing x and y (it will be either a line or a circle, depending on the equation).

And, in this course, a region will almost always be a graph of an inequality containing x and y (it's either the region above or below a line or the region inside or outside a circle, depending on the inequality).

In other words, a region is a locus where all of the (x,y) solution points form an area, instead of a line or circle.

You can start learning about graphing linear inequalities in x and y (regions above or below a line) by googling graphing linear inequalities in two variables. You will find video lectures (like Khan Academy) or written lessons (like PurpleMath).

If you need help with something you see, please start a new thread. Cheers

Thank you
i already know how to graph the inequalities ( i learn it in khan academy) but in khan academy dont explain this concepts, so thanks this really help me