Does the equation 5x2 + 5y2 = 10 represent a circle?

The general equation of a circle is given by $Ax^2 + Ay^2 + Dx + Ey + F = 0$, where $A \neq 0$. A key characteristic is that the coefficients of $x^2$ and $y^2$ must be equal and have the same sign.

The given equation is:

In this equation, the coefficient of $x^2$ is 5 and the coefficient of $y^2$ is 5. They are equal and have the same sign. There are no $x$ or $y$ terms, and no $xy$ term.

Divide the entire equation by 5:

This is the standard form of a circle centered at the origin $(0,0)$ with radius $r = \sqrt{2}$.

The equation represents a circle.

The equation $5x^2 + 5y^2 = 10$ does represent a circle.