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Introduction: A curved planar figure is a circle. Every point on the given circle is equidistant from the centre of the circle, which is a fixed point. It’s a two-dimensional form with a radius measurement. The term “circle” comes from the Latin word “circulus,” which means “little ring.” The circle represents the state of stress on separate planes in all of their orientations, with the axes representing the stress element’s major axis.
Circle
A circle is a two-dimensional shape created by a group of points on the plane that are separated by a constant or fixed distance (radius). The origin or the centre of any given circle is the fixed point, and the radius is the fixed distance between points from the origin.
Components of Circle:
To comprehend the qualities of a circle, we must first grasp its various elements or components. The main components of a circle are mention below:
Circumference: Circumference is also known as the perimeter of a circle and is defined as the distance around the circle’s edge.
Radius: The radius of a circle is the distance between its centre and any point on its perimeter. Because it is the distance from the centre and meets the circle’s perimeter at various places, a circle has numerous radii.
Diameter: A diameter is a straight line that links two locations on the circle’s periphery and passes through its center. It’s important to remember that the circle can have numerous diameters, but they must go through the middle and to have straight lines
At two unique spots that are opposite each other, touch the circle’s border.
Chord: Any line segment crossing the circle at two separate locations on its perimeter is called a chord. A circle’s diameter is the longest chord, passing through the centre and dividing it into two equal sections.
Tangent: A tangent is a line that intersects the circle at a single point but is outside the circle.
Secant: The secant is a line that connects two points on an arc or the circumference of a circle.
Arc: A circle’s arc is referred to as a curve since it is a section or portion of its circumference.
Segment: A segment in a circle is defined as the area encompassed by the chord and the matching arc in a circle. Minor segments and big segments are the two sorts of segments.
Sector: The region which contained by the 2 radius and the the arc in a circle is termed to as the sector of a circle. Sectors are divided into two categories: the minor and the major.
Locus
We are all aware that the earth travels in an elliptical orbit around the sun. The earth’s locations at different times are combined to generate an elliptical orbit.
In this situation, the locus is the arc that connects all of the earth’s locations.
Every locus (curve) has a mathematical equation known as the locus equation.
The supplied locus issue determines the curve and its equation.
What Does the term Locus Mean?
Locus can be defined as “ The term “locus” refers to a form or curve.” A group of points is known to make any shape or curve. As a result, “Locus” is a collection of points. The locus is a set of points in mathematics that meet a set of criteria.
In 2 D geometry, locus of points is a curve or a line.
Locus of a circle:
A circle is the locus of set of all the points that are at the fixed distance from a fixed point.
Here,
The term centre of any given circle is the fixed-point.
The fixed-distance is known as the “radius of the circle.”
Locus Points in two dimensional figures:
The points on the curve (or line) connected with the locus are called locus points.
Let’s look at how to determine the equation associated with each location.
Formula for Locus:
There is no specific formula for determining the locus.
The steps to finding the locus of points in two-dimensional geometry are as follows:
Consider any random point P ( x, y ) on the locus.
Create an equation based on the provided circumstance.
To get the locus equation, simplify it.
Conclusion:
A curve or other figure generated by all points meeting a certain equation of the coordinate relation, or by a point, line, or surface moving according to mathematically determined conditions is called locus. A circle is the locus of the set of all those points which are at some fixed distance from the fixed point.
