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Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
Solution:
It is given that
Directrix y = 5
Focus = (4, 1)
We know that a vertex is half of the distance between the directrix and the focus.
So the vertex here is (4, 3)
Where h = 4 and k = 3
|p| is the distance between the directrix and the vertex (p is negative as it is over the vertex)
p = -2
The equation of the parabola is
(x - h)2 = 4p (y - k)
Substituting the values
(x - 4)2 = 4 (-2) (y - 3)
(x - 4)2 = -8 (y - 3)
Therefore, the quadratic function created is (x - 4)2 = -8 (y - 3).
Using a directrix of y = 5 and a focus of (4, 1), what quadratic function is created?
Summary:
Using a directrix of y = 5 and a focus of (4, 1), the quadratic function created is (x - 4)2 = -8 (y - 3).
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