Log in to add a comment

## Answers

### This Is a Certified Answer

Certified answers contain reliable, trustworthy information vouched for by a hand-picked team of experts. Brainly has millions of high quality answers, all of them carefully moderated by our most trusted community members, but certified answers are the finest of the finest.

Locus y = f(x) or f(x,y) = c of a point (x,y) is the path taken by the point (x,y) when a certain condition or constraint is followed. Locus can also be taken as the set of all points that satisfy the given constraint.

Locus of a point (x,y) such that its distance from a fixed point (say origin) is constant is a circle, as in x² + y² = r².

In three dimensions, it is a sphere, x²+y²+z² = r²

All the points on the locus satisfy this constraint, that the distance from origin is r.

==================

Locus in three dimensions of line in 2-dimension is the curved surface that is generated or traced, when given conditions are followed.

Suppose there is a line x = a in 2-dimensions. This line is rotated around y axis in the x-z plane. Then the locus of the line (all points on the line), is a cylindrical surface with central axis as the y axis. the locus will be

x² + z² = a², for any y from -infinity to +infinity.

Locus of a point (x,y) such that its distance from a fixed point (say origin) is constant is a circle, as in x² + y² = r².

In three dimensions, it is a sphere, x²+y²+z² = r²

All the points on the locus satisfy this constraint, that the distance from origin is r.

==================

Locus in three dimensions of line in 2-dimension is the curved surface that is generated or traced, when given conditions are followed.

Suppose there is a line x = a in 2-dimensions. This line is rotated around y axis in the x-z plane. Then the locus of the line (all points on the line), is a cylindrical surface with central axis as the y axis. the locus will be

x² + z² = a², for any y from -infinity to +infinity.