Explanation:
the basic form of a circle is
(x - h)² + (y - k)² = r²
with (h, k) being the center of the circle, "r" being the radius.
when doing the multiplications of the squares :
x² - 2hx + h² + y² - 2ky + k² = r²
x² + y² - 2hx - 2ky + h² + k² - r² = 0
let's compare it to our given equation :
x² + y² + 6x - 8y + 26 = 0
x² matches
y² matches
6x = -2hx
h = -3
-8y = -2ky
k = 4
(-3)² + 4² - r² = 26
9 + 16 - r² = 26
25 - r² = 26
-r² = 1
r² = -1
r = sqrt(-1) = i
so, this is not a circle or any other curve in the world of real coordinates.