What are the vertex, focus and directrix of 9y=x2−2x+9?

1 Answer
Nallasivam V
Nov 21, 2017

Vertex (1,89)
Focus (1,11336)
Directrix y=−4936

Explanation:

Given -

9y=x2−2x+9

vertex?
Focus ?
Directrix?

x2−2x+9=9y

To find Vertex, Focus and directrix, we have to rewrite the given equation in vertex form i.e., (x−h)2=4a(y−k)

x2−2x=9y−9

x2−2x+1=9y−9+1

(x−1)2=9y−8

(x−1)2=9(y−89)

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To find the equation in terms of y [This not asked in the problem]

9(y−89)=(x−1)2

y−89=19.(x−1)2

y=19.(x−1)2+89

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Let us uses 9(y−89)=(x−1)2 to find the vertex, focus and directrix.

(x−1)2=4×94(y−89)

Vertex (1,89)

Focus (1,(89+94))
Focus (1,11336)
Directrix y=89−94
Directrix y=−4936

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