Question

Is this equation standard form of an ellipse or circle?

Answer 1

The standard form equation for a circle is

$(h-x)^2+(k-y)^2=r^2$

where (h, k) is the center and r is the radius.

The standard form equation for an ellipse is

$\frac{(x-h)^2}{a^2}} + \frac{(y-k)^2}{b^2} = 1$

(center h, k and major and minor axes a and b)

This equation is standard form for neither, but might be general form for one.

$-3x^2-3y^2-12x-12y+24=0 \\ -3(x^2+y^2+4x+4y)=-24 \\ x^2+4x+y^2+4y=8\ (complete\ the\ squares)\\ (x^2+4x+4)+(y^2+4y+4)=8+4+4\\ (x+2)^2+(y+2)^2=16 \\ Circle\ with\ radius\ 4\ and\ center\ (2,\ 2)$