What are locuses, really? (1 Viewer)

[VenomP]

My current understanding leads me to believe that it is always some point equidistant from two different equation-lines. But I know there are some questions which specifically state that the equidistance is a condition of the locus.

So what is a locus, really?

Also, can anyone tell me the formula for an external and internal division and all that jazz?

Thanks.

 

[Drongoski]

My current understanding leads me to believe that it is always some point equidistant from two different equation-lines. But I know there are some questions which specifically state that the equidistance is a condition of the locus.

So what is a locus, really?

Also, can anyone tell me the formula for an external and internal division and all that jazz?

Thanks.

Roughly:

A locus is the path of a point that satisfies a set of conditions (e.g. distance from a given fixed point is 3 x it's distance from a fixed line). In obtaining an equation of the locus, or some equivalent statement of relationships, we obtain an expression of the relationship.

e.g. the locus of a point 8 units away from a fixed point (5, -7) is
the equation of the circle: (x-5)^2 + (y+7)^2 = 8^2

Note: The plural for locus is loci .

 

[kurt.physics]

My current understanding leads me to believe that it is always some point equidistant from two different equation-lines. But I know there are some questions which specifically state that the equidistance is a condition of the locus.

So what is a locus, really?

Also, can anyone tell me the formula for an external and internal division and all that jazz?

Thanks.

A locus is the description of a moving point that satisfy certain conditions. One of the most commonly used conditions for questions regarding locus is the point being equidistant from 2 other points or lines.

But this is not the only condition possible for locus, you can have a point that is always x units away from the point (a,b). Or you could have the condition that the sum of the distances r and q from the point P(x,y) is a constant.

 

[kurt.physics]

Also, can anyone tell me the formula for an external and internal division and all that jazz.

 

[Trebla]

The very idea of a "moving" point might confuse a lot of people lol.

A locus is a set of points that satisfy a certain condition. This set of points can be described by an equation.

So for example say you want the locus of points such that the shortest distance to the x-axis is equal to the shortest distance to the y-axis.
Some points that satisfy this condition are (1, 1), (- 3, - 3) or (69, 69). More generally to describe EVERY point that satisfies this condition, it is simply the equation y = x, which accounts for the whole set of points of the locus.

 

[youngminii]

Lol my old maths teacher used to say 'Just replace the word locus with equation'.

 

[jet]

The very idea of a "moving" point might confuse a lot of people lol.

A locus is a set of points that satisfy a certain condition. This set of points can be described by an equation.

So for example say you want the locus of points such that the shortest distance to the x-axis is equal to the shortest distance to the y-axis.
Some points that satisfy this condition are (1, 1), (- 3, - 3) or (69, 69). More generally to describe EVERY point that satisfies this condition, it is simply the equation y = x, which accounts for the whole set of points of the locus.

Completely true. Set of points is a better way of saying it.

 

[duckcowhybrid]

A Locus is a set of points that satisfies a certain condition. It can always be written as an equation. Basically if there's the word locus think: what is the equation of the curve that is .........