Answer:
Step-by-step explanation:
Focus: (6,4)
Directrix lies 6 units below the focus, so the parabola opens upwards and focal length p = 6/2 = 3.
The equation of the directrix is y = -2.
The vertex is halfway between focus and directrix, at (6,1).
Equation of the parabola:
y = (1/(4p))(x-6)²+1 = (1/12)(x-6)²+1
The equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Parabolas are used to represent a quadratic equation in the vertex form
The given parameters are:
Focus = (6,4)
Directrix (x) = 6 units below the focus,
Start by calculating the focal length (p)
[tex]p = \frac x2[/tex]
This gives
[tex]p = \frac 62[/tex]
[tex]p = 3[/tex]
Next, calculate the vertex as follows:
[tex](h,k) = (6,2/2)[/tex]
Simplify
[tex](h,k) = (6,1)[/tex]
The equation of the parabola is then calculated a:
[tex]y = \frac{1}{4p}(x - h)^2 + k[/tex]
So, we have:
[tex]y = \frac{1}{4*3}(x - 6)^2 + 1[/tex]
Simplify
[tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
Hence, the equation of the parabola is [tex]y = \frac{1}{12}(x - 6)^2 + 1[/tex]
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