How to write this conic equation in standard form? $$x^2+y^2-16x-20y+100=0$$
Standard form? Circle or ellipse?

Recall that one of the usual standard forms is:
$(x - a)^{2} + (y - b)^{2} = r^{2}$ where...


*

*(a,b) is the center of the circle

*r is the radius of the circle


Rearrange the terms to obtain:
$x^{2} - 16x + y^{2} - 20y + 100 = 0$
Then, by completing the squares, we have:
$(x^{2} - 16x + 64) + (y^{2} - 20y + 100) = 64$
$(x - 8)^{2} + (y - 10)^{2} = 8^{2}$
Thus, we have a circle with radius $r = 8$ and center $(a,b) = (8,10)$
