Final answer:
(y - 5)^2 = 8(x - 2)
The equation of a parabola that opens to the left, with a vertex at (2, 5) and 2 units away from the focus is (y - 5)^2 = 8(x - 2).
Step-by-step explanation:
To write the equation of a parabola that opens to the left, with a vertex at (2, 5) and is 2 units from the focus, we can use the standard form of the equation for a horizontal parabola. Since the parabola opens to the left, the equation will be of the form:
(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. Since the vertex is at (2, 5) and the focus is 2 units away, p is -2 because the parabola opens to the left. Plugging in these values, we get:
(y - 5)^2 = -4(-2)(x - 2)
Simplifying, the equation of the parabola is:
(y - 5)^2 = 8(x - 2)