Identify the focus and directrix If this parabola

Question

Y^2-8x+10y+9=0

Answer 1

Rewrite the equation in conic form:  y² - 8x + 10y + 9 = 0. --> 8x - 9 = y² + 10y = y² + 10y + 25 - 25. --> 8x + 16 = (y + 5)² --> 8(x + 2) = (y + 5)²

4p = 8 --> p = 2

Vertex is (-2, -5)

Focus is (-2+2, -5) --> (0, -5)

Directrix is x = -2-2 --> x = -4