Hi, re TY, note ommission on the minus.

x^2-2x+8y+9=0

  V(1,-1), 4p=8, p = 2 F(1,-3) 

  a = (-1/8) < 0    Parabola opens downward

Directrix y  = 1 and x = 1 is the axis of symmetry

 

  

See below descriptions of various conics                         

Standard Form of an Equation of a Circle is  

where Pt(h,k) is the center and r is the radius





 Standard Form of an Equation of an Ellipse is  where Pt(h,k) is the center. (a positioned to correspond with major axis)

 a and b  are the respective vertices distances from center and ±are the foci distances from center: a > b



Standard Form of an Equation of an Hyperbola opening right and  left is:

   where Pt(h,k) is a center  with vertices 'a' units right and left of center.



Standard Form of an Equation of an Hyperbola opening up and down is:

   where Pt(h,k) is a center  with vertices 'b' units up and down from center.



the vertex form of a parabola opening up or down,  where(h,k) is the vertex.

The standard form is , where  the focus is (h,k + p)



the vertex form of a parabola opening right or left,  where(h,k) is the vertex.

The standard form is , where  the focus is (h +p,k )

 

Answer by lwsshak3(11628)   (Show Source): You can put this solution on YOUR website!
 How do you find the vertex, focus, directrix, and axis of symmetry of the parabola? 

x^2-2x+8y+9=0

complete he square

(x^2-2x+1)+8y+9-1=0

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

(x-1)^2=-8(y+1)

This is an equation of a parabola that opens downwards

Form of equation: (x-h)^2=-4p(y-k), (h,k)=(x,y) coordinates of vertex

For given equation:

vertex:(1,-1)

axis of symmetry: x=1

4p=8

p=2

focus: (1,-1-p)=(1,-1-2)=(1,-3) (p units below vertex on axis of symmetry)

directrix: y=-1+p=-1+2=1 (p units above vertex on axis of symmetry) 

Answer by John10(297)   (Show Source): You can put this solution on YOUR website!
 Hint:

Convert your equation in form: (x - h)^2 = 4p(y - k)



where 



(h,k) is the vertex

(h, k + p) is the focus

y = k - p is the directrix

x = h is the axis of symmetry



I'll help you to convert it:

x^2 - 2x + 8y +9 = 0

x^2 - 2x + 1 = -8y - 8

(x - 1)^2 = -8( y + 1)



You can follow up from here. Good luck:)



John10

 

RELATED QUESTIONS

How do you find the focus, directrix, and vertex of the formula : x^2+8y=0... (answered by lwsshak3)

How do you find the vertex, value of p, axis of symmetry, focus, and directrix of each... (answered by josgarithmetic)

I need to find the vertex, focus, directrix and axis of symmetry of the parabola:... (answered by lynnlo)

Find the vertex, focus, and directrix of the parabola and graph it.... (answered by venugopalramana)

How do you find the Vertex, focus, directric of the parabola and sketch its graph for the  (answered by stanbon)

Give the focus, directrix, and axis of symmetry for the parabola... (answered by lwsshak3)

find the properties of parabola: y^2=x
vertex:
axis of symmetry
focus
directrix... (answered by josgarithmetic)

Please help me find the axis of symmetry, the focus, directrix and vertex of the... (answered by stanbon)

How do I find the vertex, focus, directrix, axis of symmetry, 
and latus rectum of this... (answered by Edwin McCravy)