Final answer:
A parabola with a focus of (8,3) and a directrix of x=10 opens towards the left because the focus is left of the directrix.
The vertex is located at the midpoint between the focus and directrix, thus the vertex would be at (9, 3).
The standard equation of the parabola is (y-3)² = -4(x-9).
Step-by-step explanation:
A parabola can be drawn given a focus of (8,3) and a directrix of x=10. The directrix is a vertical line, and the focus is a point to the left of it, this implies that the parabola opens towards the left.
For a parabola, the distance from any point on the curve to the focus is equal to the distance from that point to the directrix.
Therefore, the vertex of the parabola will be located at the midpoint between the focus and the directrix on the horizontal line that crosses the focus.
In this case, since the directrix is x=10 and the x-coordinate of the focus is 8, the vertex will be at (9, 3).
The standard equation of a parabola that opens left or right is (y-k)² = -4p(x-h), where (h, k) is the vertex of the parabola and p is the distance from the vertex to the focus (which would be negative if the parabola opens to the left as it does in this scenario), with the vertex at this midpoint. In this case, p = -1.
Therefore, the equation of our parabola would be (y-3)² = -4(x-9).