Question

3x^2 + 3y^2 + 12x -9y + 12 =0
This is the equation of a circle in an XY pane. What is the diameter? Please explain.

Answer 1

first we will divide the whole equation by 3
because we need coefficients of x^2 and y^2
so we get our new equation
${x}^{2} + {y}^{2} + 4x - 3y + 4$
now the radius of circle can be given by
$\sqrt{ {g}^{2} + {f}^{2} - c }$
where g = -(coefficient of x)/2
and f = -(coefficient of y)/2
and c is constant = 4
√{ (2^2) + (3/2)^2 - 4 }
3/2
now radius is = 1.5 units
& diameter is 3 units