Locus of a point in mathematics

Locus :-

If a point travels according to the given condition then path created by point is known as the locus of that point.

Or locus is a geometric shape where every point satisfies the given condition.

Equation of the locus:

A algebraic relations got from the geometric condition for any variable point (x,y) is known as equation of the locus.

Example:-

Find the locus of a point, which is always at equal distance from two points (-1,2) and (4,0).

Let the coordinate that point is P(h,k).

Now according to the given condition

Distance from p(h,k) to (-1,2) = distance from P(h,k) to (4,0)

$\sqrt{(h+1)^2 +(k-2)^2} = \sqrt{√(h-4)^2+(k-0)^2}$

$(h+1)^2 +(k-2)^2 = (h-4)^2+(k-0)^2$

$h^2+2h+1 + k^2 -4k +4 = h^2 -8h + 16 +k^2$

$2h+1-4k +4 +8h - 16 = 0$

$10h -4k - 11 =0$

So locus of point p(h,k) is $10x - 4y -11 =0$

Locus of a point (mathematics)