By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)
How to locate the focus of a parabola
The standard equation of the parabola with an horizontal axis of symmetry is presented below:
[tex]x - h = \frac{1}{4\cdot p}\cdot (y - k)^{2}[/tex] (1)
Where:
- h, k - Vertex of the parabola.
- p - Distance between the vertex and the focus.
The coordinates of the focus is described by the following expression:
F(x, y) = (h + p, k)
If we know that h = 5, k = - 1 and p = - 2, then the coordinates of the focus are:
F(x, y) = (5 - 2, - 1)
F(x, y) = (3, - 1)
By definition of the focus of a parabola, the coordinates of the focus of the parabola - 8 · (x - 5) = (y + 1)² are represented by the point F(x, y) = (3, - 1). (Correct choice: A)
To learn more on parabolas: https://brainly.com/question/21685473
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