The general form of the equation for the given circle is
<h2>Further Explanation:</h2><h3>Equation of circle </h3>
- An equation of a circle is calculated when the radius of a circle and the coordinates of its center are known or can be calculated.
- Equation of a circle can be written in two forms namely; the standard and the general form.
<h3>Standard form</h3>
- Standard form of Equation of a circle is written as:
- Where (a,b) is the center of the circle and r is the radius of the circle.
- When an equation is written in this form the center and the radius can easily be identified from the equation, with radius always being positive.
<h3>General form </h3>
- The general form of an equation of a circle is given by;
; where d, e and f are constants.
- When an equation is written in this form one has to use the completing square method to write it in standard form so as to identify the center and the radius.
In our case;
a)
Using completing square method, the standard form will be;
With the center (4,4) and radius of 3 units
b)
Standard form;
This is not an equation of a circle
c)
Standard form:
Is not a circle
d)
Standard form:
It is not a circle
Therefore;
The general form of the equation of the circle can only be;
Keywords: Circle, equation of the circle, center, radius
<h3>Learn more about:</h3>
Level: High school
Subject: Mathematics
Topic: Equation of the circle