If you want to set points via some algebraic equation, then you are probably doing the equation of line. So, the equation of a line is setting the points with an algebraic equation, which forms a line in a coordinate system. There are numerous points that are placed together known as the variables which are represented as x and y. These variables are then applied in the form of an algebraic equation.
So, what does the equation of line confirm? The equation of line confirms whether or not the points in consideration are set on a line or not.
Students must remember that the equation of a line is a type of linear equation with a degree as in one.
Table of Contents
How Can You Form the Equation of a Line?
The equation of a line can be formed by making a slope of the line and a specific point on the line. First, we are required to understand this slope of the line and the specific point on the line, in order to better understand the formation of the equation of the line.
The slope can be defined as nothing but an inclination of the line with the positive axis as an x-axis which is expressed as a numeric integer, fraction, or like the tangent of the angle which will make the positive x-axis. The point is referred to as the point in the coordinate system with the x coordinate and the y coordinate in place.
What is the Standard Form of Equation?
The standard form of the equation of a line can be stated as ax + by + c = 0. In this case, a and b are the coefficients while a and y are the variables and c is the constant here.
This equation is degree one, x and y being its variables. The values of x and y will represent the coordinating points on the line which is represented in the coordinate plane. Check out the important points which are required in writing the standard form of the equation.
- First write the x term, then the y term, and then write the constant term.
- The constant and the coefficient terms cannot be written in the form of fractions, decimals. It should be written in the form of integers.
- The value of a and the x coefficient is to be written as the positive integer.
What Will be the Equation of Circle?
The equation of a circle is a description of the circle in an algebraic way. This equation will describe the circle which has the length and the radius of the circle. Students must not get confused between the equation of the circle and the formula of the circumference of the circle, both are specific in their measurement. The equation of circle is very much necessary in coordinate geometry.
A circle is to be drawn on a piece of paper. We can draw the circle if only we know the center and radius of the circle. Thus, a radius can be represented in many other forms:
- In the general form
- In the standard form
- In the parametric form
- In the polar form
Lay Out the Equation of Circle
In a Cartesian Plane, an equation of circle represents where it is located. If we know the central position of the circle and the coordinates of the circle, we can easily frame the equation of a circle. The equation of a circle is the image of the points on the circumference of the circle.
We know a circle is a representation of the locus of the points whose distance from the fixed point has a constant value. This is the center of the circle, and the constant value is actually the radius of the circle.
So, the standard equation of circle at the center placed at (x1,y1) and radius r is – (x−x1)2+(y−y1)2=r2.
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