circle
The locus of points at a given distance to a line would be a line parallel to the first line. Assuming that both lines are straight.
There are several ways of defining a parabola. Here are some:Given a straight line and a point not on that line, a parabola is the locus of all points that are equidistant from that point (the focus) and the line (directrix).A parabola is the intersection of the surface of a right circular cone and a plane parallel to a generating line of that surface.A parabola is the graph of a quadratic equation.
triangle
Join the centre of the circle O and the point A .Extend it to both sides to form a line.This is the required locus
parabola
An ideal line also known as the locus of an ideal point
The locus point is the perpendicular bisector of AB. The locus point is the perpendicular bisector of AB.
A line is the locus of points such that the gradient (slope) between that point and one fixed point in the plane is a constant. Technically, that definition does not include a vertical line because its gradient is not defined! You could get around that this by requiring that either the gradient is a constant or, if it is undefined, then the inverse gradient (dx/dy) is constant.
The locus of a point is the set of all positions that the point can occupy where it satisfies some defining function.
It is the locus of all points such that their distance from a fixed line (the directrix) is the same as their distance from a fixed point which is not on that line (the focus).
You find the locus of the point over time and either through geometrical or algebraic reasoning demonstrate that the result is a straight line.
The locus of a moving point so that it is equidistant from another fixed point (i.e. the distance between them is always constant) is a circle.
It is going to look like a somewhat of a quadratic parabola.
circle
Given a straight line (a directrix) and a point (the focus) which is not on that line, a parabola is locus of all points whose distance form the directrix is the same as its distance from the focus.
The center isn't the locus, and a point on the circumference isn't the locus.The whole circumference of the circle is the locus.It's the locus of all points that have the same distance from the center of the circle.