SOLUTION: Sketch the curve, find the coordinate of the vertex and focus, and find the equation of the axis and directrix of x^2 - 6x + 8y + 25 = 0

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Sketch the curve, find the coordinate of the vertex and focus, and find the equation of the axis and directrix of x^2 - 6x + 8y + 25 = 0      Log On


   

Question 1119534: Sketch the curve, find the coordinate of the vertex and focus, and find the equation of the axis and directrix of x^2 - 6x + 8y + 25 = 0
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


The equation has an x^2 term; the parabola opens either up or down. The general form of the equation is

y-k+=+%281%2F%284p%29%29%28x-h%29%5E2

where (h,k) is the vertex and p is the directed distance from the directrix to the vertex and from the vertex to the focus.

x%5E2-6x%2B8y%2B25+=+0
x%5E2-6x+=+-8y-25
x%5E2-6x%2B9+=+-8y-25%2B9+=+-8y-16
%28x-3%29%5E2+=+-8%28y%2B2%29
y%2B2+=+%28-1%2F8%29%28x-3%29%5E2
y-%28-2%29+=+%281%2F%284%28-2%29%29%29%28x-3%29%5E2

This is in the required form. The vertex is (3,-2); p = -2.

With vertex (3,-2) and p=-2, the focus is at (3,-4); the directrix is y=0; and the axis is x=3.

A graph...

graph%28400%2C400%2C-5%2C10%2C-10%2C5%2C%28-1%2F8%29%28x-3%29%5E2-2%29