jmc

This looks like the equation of a circle, but we have replaced $x$ with $\frac{x}{2}$. So, we suspect this equation defines an $\boxed{\text{ellipse}}$. To verify this we write $${\left(\frac{x}{2}-3\right)}^2=\frac{1}{4}{\left(x-6\right)}^2,$$and we see that the equation $$\frac{{\left(x-6\right)}^2}{4}+y^2=10$$is the equation of an ellipse.