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.

if anyone could please answer it. thank you.

#Geometry

Easy Math Editor

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Comments

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.

Kushal Dey - 1 year, 2 months ago

Math	Appears 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}`	$\boxed{123}$