What is the equation of the parabola with vertex (4, 4) and focus ( 7 , 4)?
(1 point)
x = 1/12 * (y - 4) ^ 2 + 4
x = 1/6 * (y - 4) ^ 2 + 4
y = 1/12 * (x - 4) ^ 2 + 4
y = 1/6 * (x - 4) ^ 2 + 4
To find the equation of a parabola with a given vertex (h, k) and focus (h + c, k), we can use the formula (x - h)^2 = 4p(y - k).
In this case, the vertex is (4, 4) and the focus is (7, 4). This means that the vertex is located at (h, k) = (4, 4) and the focus is located at (h + c, k) = (7, 4).
From this information, we can determine the value of p, which is the distance from the vertex to the focus. Since the vertex is (4, 4) and the focus is (7, 4), p = 3.
Now we can plug in the values for h, k, and p into the formula (x - h)^2 = 4p(y - k) to find the equation of the parabola:
(x - 4)^2 = 4(3)(y - 4)
(x - 4)^2 = 12(y - 4)
(x - 4)^2 = 12y - 48
(x - 4)^2 = 12y - 48
x^2 - 8x + 16 = 12y - 48
x^2 - 8x + 16 - 12y + 48 = 0
x^2 - 8x - 12y + 64 = 0
Therefore, the equation of the parabola with vertex (4, 4) and focus (7, 4) is:
x^2 - 8x - 12y + 64 = 0