# locus

hi! I am having a problem understanding what locus actually mean? where do we use it?

1.there is one sum which was given as an example, I really did not understand what is the need for rotating and translating the plane in this sum. the sum is; Find the locus of points
PP
P such that the sum of the squares of the distances from
P P
P to
A A
A and from
P P
P to
B, B,
B, where
AA
A and
BB
B are two fixed points in the plane, is a fixed positive constant.

After rotating and translating the plane, we may assume that
A=(−a,0) A = (-a,0)
A=(−a,0) and
B=(a,0).B = (a,0).
B=(a,0). Suppose the constant is
c2, c^2,
c........what is the need for transformation of the axes

2.an iron rod of length 2l is sliding on two mutually perpendicular lines. find the locus of the midpoint of the rod. in this question the equation of locus is x^2+y^2=l^2, which is the equation of a circle but how does it form a circle. 9 months, 2 weeks ago

This discussion board is a place to discuss our Daily Challenges and the math and science related to those challenges. Explanations are more than just a solution — they should explain the steps and thinking strategies that you used to obtain the solution. Comments should further the discussion of math and science.

When posting on Brilliant:

• Use the emojis to react to an explanation, whether you're congratulating a job well done , or just really confused .
• Ask specific questions about the challenge or the steps in somebody's explanation. Well-posed questions can add a lot to the discussion, but posting "I don't understand!" doesn't help anyone.
• Try to contribute something new to the discussion, whether it is an extension, generalization or other idea related to the challenge.

MarkdownAppears as
*italics* or _italics_ italics
**bold** or __bold__ bold
- bulleted- list
• bulleted
• list
1. numbered2. list
1. numbered
2. list
Note: you must add a full line of space before and after lists for them to show up correctly
paragraph 1paragraph 2

paragraph 1

paragraph 2

[example link](https://brilliant.org)example link
> This is a quote
This is a quote
    # I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
# I indented these lines
# 4 spaces, and now they show
# up as a code block.

print "hello world"
MathAppears as
Remember to wrap math in $$ ... $$ or $ ... $ to ensure proper formatting.
2 \times 3 $2 \times 3$
2^{34} $2^{34}$
a_{i-1} $a_{i-1}$
\frac{2}{3} $\frac{2}{3}$
\sqrt{2} $\sqrt{2}$
\sum_{i=1}^3 $\sum_{i=1}^3$
\sin \theta $\sin \theta$
\boxed{123} $\boxed{123}$

Sort by:

Locus means the path traced by a variable point, which moves in the XY plane under certain, geometric or algebraic conditions. In this question, you are basically to find out the locus of a point whose sum of distances from two fixed points is constant. This locus is called an ellipse and the most general established equation of an ellipse is x^2/a^2+y^2/b^2=1. You may google up the word "ellipse" for further reading.

- 6 months, 2 weeks ago