Final answer:
The equation of the parabola in standard form whose focus is at (-10, -1) and directrix is the line x = -8 is y² + 2y = 8x + 79.
Step-by-step explanation:
The equation of the parabola in standard form whose focus is at (-10, -1) and directrix is the line x = -8 can be found using the following formula:
(x - h)² = 4p(y - k)
where (h, k) is the vertex and p is the distance between the vertex and the focus or directrix.
In this case, the vertex is (-10, -1) and the directrix is x = -8. Since the directrix is a vertical line, the parabola opens horizontally. Therefore, the equation of the parabola is:
(y + 1)² = 4(2)(x + 10)
Simplifying the equation gives:
y² + 2y + 1 = 8x + 80
So, the equation of the parabola in standard form is:
y² + 2y = 8x + 79