Question

The equation x^2+y^2+3x-2y=0 is an example of ?

Answer 1

The equation x^2+y^2+3x-2y=0 is an example of ?

We can say that this equation is the circle equation.

$\begin{gathered} \mleft(x-a\mright)^2+\mleft(y-b\mright)^2=r^2,\mathrm{\: with\: a\: radius\: r,\: centered\: at}\: \mleft(a,\: b\mright) \\ \end{gathered}$

Using the form standard equation circle equation:

$\mleft(x-\mleft(-\frac{3}{2}\mright)\mright)^2+\mleft(y-1\mright)^2=\mleft(\frac{\sqrt{13}}{2}\mright)^2$

Therefore,

$\mleft(a,\: b\mright)=\mleft(-\frac{3}{2},\: 1\mright)$

and

$r=\frac{\sqrt{13}}{2}$

Answer: The given equation is an example of the circle equation.