What are loci? What is loci and symmetry? How do you use them? Do they have any specific formulae to work with? What are they used for? Please help!

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aruv | High School Teacher | (Level 2) Valedictorian

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Locus is path described by the point under given condition. Loci is plural form of the word locus.

For example  for defining circle, we say a point is moving in such a way that always remains equidistance from a  fixed point. Here fixed point is known as center and the path described by the point is circumference of the circle.

Let P(x,y) is moving point. C(x1,y1) is fixed point .

`sqrt((x-x_1)^2+(y-y_1)^2)=r`

`(x-x_1)^2+(y-y_1)^2=r^2`

This is locus of moving point P.

Symmetry you can say image (congruence ) of the object . For example You left palm and right palm are symmetrical.

Symmetry we apply to siplify /visualise the problem  and to avoid repitition.

No there are no specific formulas for these. Either for locus or for symmetry conditions prescribed in advance.