What are the vertex, focus and directrix of # y=(x + 6)^2/36+3 #?

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Answer 1 · 2017-11-07T23:25:12

Given: #y=(x + 6)^2/36+3#

The vertex form is:

#y = 1/(4f)(x - h)^2 + k#

Writing the given equation in that form:

#y=1/36(x - (-6))^2+3#

Matching terms and factors:

#4f = 36#

#f = 9#

#h = -6#

#k = 3#

The vertex is:

#(h,k)#

#(-6,3)#

The focus is

#(h,k+f)#

#(-6,3+9#

#(-6,12)#

The directrix is:

#y = k-f#

#y = 3 - 9#

#y = -6#