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Find the focus and directrix of the following parabola:
(y−4)²=16(x−6)
Focus: (10, [?])

Sagot :

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Step-by-step explanation:

The given parabola is in the form (y - k)² = 4p(x - h), where (h, k) is the vertex and p is the distance from the vertex to the focus.

Comparing the given equation (y - 4)² = 16(x - 6) with the standard form, we can identify:

h = 6

k = 4

4p = 16

Divide by 4:

p = 4

The focus is p units to the right of the vertex (since the parabola opens to the right), so the focus is:

(6 + 4, 4) = (10, 4)

Therefore, the focus is (10, 4).

To find the directrix, we need to know that the directrix is p units to the left of the vertex (since the parabola opens to the right). So, the directrix is:

x = h - p

= 6 - 4

= 2

The equation of the directrix is x = 2.

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