Completing the square to find centre and radius of a circle

Question

$x^2 + y^2 -2x - 5y + 16 = 0$

So I went like this: $$x^2 - 2x + 1 - 1 + y^2 - 5y + \frac{25}{4} - \frac{25}{4} = - 16 \\ (x-1)^2 + (y-\frac{5}{2})^2 = -\frac{64}{4} + \frac{25}{4} + \frac{4}{4}$$

I think you can see where i'm going with this...

Answer 1

The two steps of calculation you made are both correct. Now it's time to review what you made.

You have proven that there exists no pair of real values $(x,y)$ that satisfies the equation. Therefore, the equation is not an equation of a circle.