The given equation is an equation of a circle because it looks similar to the general equation of a circle.
What is the general equation of a circle?
The general equation of a circle is:
x² + y² +2gx + 2fy + c = 0...........eq1
Where (-g, -f) is the center of the circle.
c is a constant
Given equation is
3x² +6x + 3y²+7y+4 = 0
Let us take 3 as common
x² + 2x+y²+7/3y + 4/3 = 0
Let us rearrange the equation
x² + y²+2x +7/3y + 4/3 = 0...........eq2
Now look at eq1 and eq2
We got that eq2 is having a similar pattern as eq1.
Therefore, The given equation is an equation of a circle.
To get more about circle visit:
https://brainly.com/question/1506955
