# What are the vertex, focus and directrix of # 9y=x^2-2x+9 #?

##### 1 Answer

Nov 21, 2017

Vertex

Focus

Directrix

#### Explanation:

Given -

#9y=x^2-2x+9#

vertex?

Focus ?

Directrix?

#x^2-2x+9=9y#

To find Vertex, Focus and directrix, we have to rewrite the given equation in vertex form i.e.,

#x^2-2x=9y-9#

#x^2-2x+1=9y-9+1#

#(x-1)^2=9y-8#

#(x-1)^2=9(y-8/9)#

==================

To find the equation in terms of

#9(y-8/9)=(x-1)^2#

#y-8/9=1/9.(x-1)^2#

#y=1/9.(x-1)^2+8/9#

================

Let us uses

#(x-1)^2=4 xx 9/4(y-8/9)#

Vertex

Focus

Focus

Directrix

Directrix