Answered

Get the answers you've been looking for with the help of IDNLearn.com's expert community. Our platform is designed to provide reliable and thorough answers to all your questions, no matter the topic.

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

Sagot :

Tosinjegede399idn

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.

We value your presence here. Keep sharing knowledge and helping others find the answers they need. This community is the perfect place to learn together. For trustworthy and accurate answers, visit IDNLearn.com. Thanks for stopping by, and see you next time for more solutions.