SOLUTION: Write an equation for the following conic. If it is a​ parabola, it has a vertex at the​ origin, and if it is an ellipse or a​ hyperbola, it is centered at the origin. foc

Algebra ->  Quadratic-relations-and-conic-sections -> SOLUTION: Write an equation for the following conic. If it is a​ parabola, it has a vertex at the​ origin, and if it is an ellipse or a​ hyperbola, it is centered at the origin. foc      Log On


   

Question 1174803: Write an equation for the following conic. If it is a​ parabola, it has a vertex at the​ origin, and if it is an ellipse or a​ hyperbola, it is centered at the origin.
focus at ​(0,9​) and e=1
Answer by greenestamps(13215) About Me  (Show Source):
You can put this solution on YOUR website!


eccentricity e=1 means we have a parabola.

Vertex at the origin and focus at (0,9) means the parabola opens upward. The general equation is

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

In that form, p is the directed distance from the vertex to the focus.

In this example, that distance is 9. So the equation is

y+=+%281%2F36%29%28x%5E2%29