LOCUS VARIOUS FORMS OF LINES

LOCUS VARIOUS FORMS OF LINES
Lous Definition: A set of points which satisfy  a given condition or conditions is called a  Locus
Example: A Locus of points which are equidistant from a fixed point in a plane is called a circle.

This fixed point is called,"The centre of from the circle" and the fixed distance is called," The radius of the Circle.
NOTE: A Locus of points usually results in a curve or surface
Six Important Locus Theorems
Theorem I: The points at the fixed distance ‘r’ from the point 'p' is considered to be a circle with ‘r’ as its radius and centre p.

Theorem 2:The Locus at a fixed distance 'd' from the line 'm’ is considered as a pair of parallel lines that are located on either side of 'm’ at a distance "d" from the Line m

Theorem 3: The Locus which is equidistant from the two  given points Say A and B, are Considered as perpendicular bisectors of the line segment that joins the two points.

Theorem 4: The Locus which is equidistant from the two parallel lines say m₁ and m₂ is considered to be a line parallel to both the lines m₁ and m₂  it should be halfway between them.

Theorem 5: The Locus which is present on the interior of an angle equidistant from the sides of an angle is considered to be the bisector of the angle

Theorem 6: The Locus which is equidistant from the two intersecting lines say  m₁ and m₂   is considered to be a pair of Lines that bisects the angle produced by the two lines m₁ and m₂