Before discussing the equation of a circle, it will be logical enough for us to discuss ‘what is a circle?’ A circle can be defined as a set of various points which are being placed equally from a fixed point in the plane of the figure. This fixed point is named the ‘center’ of the circle. The circumference is known as the length of the circle. So, the distance between the center and the circumference of the circle is called the radius. Now we are set to know the equation of a circle.
A circle as known is a closed curve that is being drawn from the fixed point known as the central part, this is the point when all the points on the curve have an equal distance from the central point to its center. The equation of a circle with ‘r’ being the radius is given by:
(x-h)2 + (y-k)2 = r2
This is the standard and accepted form of the equation. So, it means that if the coordinates and radius of the circle are given then we can easily find the equation of the circle.
Example: Suppose there are two points on the circle – 1,2 and the radius is equal to 4 cm. Then this will be the following equation of the circle:
(x-1)2+(y-2)2 = 42
(x2−2x+1) + (y2−4y+4) =16
X2+y2−2x−4y-11 = 0
Equation of Line
The equation of a line can be constructed with the help of a slope of a definite line and with a point on the line. We will understand more about the slope of the line and the required point on the line. In order to better understand the formation of the equation of line, we must understand that the line is inclined with the positive x-axis which is expressed as a numeric integer, fraction, or simply as a tangent of the angle; this makes a positive x-axis on the plane. This point refers to a point which is the coordinate system with the x coordinate and of the y coordinate
Standard Form of Equation of a Line
The basic and the standard form of the equation of a line can be represented as ax + by + c = 0.
In this case, a, b, are the coefficients of the x, y which are the variables, and c is the constant indicator here. This is an equation of a single with the variables of x and y. The values of x and y are represented as the coordinating points on the line that is represented in a coordinate plane. We are providing a summary of quick rules that are to be followed in the process of writing the equation of a line.
The x term should be written at the beginning, after which it is followed by the y-term, and this finally is to be written in the form of a constant term which is written thereby.
The coefficients and the constant values of this line are also written in the form of fractions, decimals, or integers.
The value of ‘a is the coefficient of x which is always written in the form of a positive integer.
In the equation of the line which is ax + by + c = 0,
- a, b are the coefficients
- x, y is called the variables
- while c is the constant here
Different Forms of Equation of a Line
In this section, we will know about five basic different forms of writing the equation of the line which is mainly based on the parameters that are already known for the straight line. The different forms of this are used to find and represent the equation of a line which are given as below:
- Point Slope Form
- Two Point Form
- Slope-intercept form
- Intercept form
- Normal form
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