Question 1: Find the vertex, focus, and directrix of the parabola:
4x - y^2 - 2y - 33 = 0
My work:
y^2 + 2y = 4x - 33
(y + 1)^2 = 4(x - 8)
Vertex: (8, -1); Focus: (-7, -1); Directrix: x = -9
Question 2: Find the vertex, focus, and directrix of the parabola:
x^2 - 2x + 8y + 9 = 0
My work:
8y = -(x^2 - 2x + 9)
8y = -(x - 1)^2 - 8
8(y + 1) = -(x - 1)^2
Vertex: (1, -1); Focus: (0, -1); Directrix: x = -2
I am not sure if my work is correct, especially in the 2nd question. Can you please tell me if I went wrong?
Thanks!