Question

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Given the directrix = 6 and the focus (3Ė-5) , what is the vertex form of the equation of the parabola?
)²
The vertex form of the equation is 2 =
(y +

Answer 1

The vertex form of the equation for a parabola with its vertex at the point (h, k) and the focus at (h, k + p) or (h, k - p) is:

(y - k)² = 4p(x - h)

In this case, the focus is (h, k + p) = (3, -5), and the directrix is y = 6.

The value of p can be found as the distance from the focus to the directrix. It's the absolute value of the difference in the y-coordinates:

p = |-5 - 6| = 11

Now, we can use these values in the vertex form equation:

(y - k)² = 4p(x - h)

(y - (-5))² = 4(11)(x - 3)

(y + 5)² = 44(x - 3)

So, the vertex form of the equation of the parabola is:

(y + 5)² = 44(x - 3)