Suppose I have a curve, in this case it's a parabola, and I've to find the points through which this curve always pass. The equation of the curve is $$\left\{x-\frac{a}{2}(1+\sqrt3)\right\}^2+\left\{y-\frac{a}{2}(1+\sqrt3)\right\}^2=\frac{(x+y+a)^2}{2}$$
Since it was a MCQ I was able to get the right answer by putting in the values. But I want to know whether there is a proper method for these type of questions or not. The answers were $(a,0)$ and $(0,a)$.
Any help is greatly appreciated.