Complete the square.
can you show how , i'm lost
x^2 + 20x - 4y + 100 = 0

Ignore the -4y term for now. Only focus on x^2+20x+100. This can be factored to (x+10)^2. Notice how expanding it out gives

(x+10)^2 = (x+10)(x+10) 
(x+10)^2 = x(x+10) + 10(x+10)
(x+10)^2 = x^2+10x + 10x + 100
(x+10)^2 = x^2 + 20x + 100

So this means
x^2+20x-4y+100 = 0
turns into
(x+10)^2 - 4y = 0
after we factor

The second equation listed above implies that we have a parabola because we can solve for y to get
-4y = -(x+10)^2
y = (1/4)(x+10)^2