I have more questions, sorry to bother
they ask me to write the equation in standard form, then find the center and radius x^2+y^2+8x+7= 0
they also ask me to find the vertex, focus and the lenght of the lactus rectum 8y=x^2
and just one last, so sorry to ask for that much help
find the equation of the parabola that has a focus at (-3,4) and directriz y=2
the general form of your parabola is: . This is a parabola which opens up and has it's vertex at V(0, 0). The focus has the (general) coordinates . With your equation it becomes: .
The lactus rectum is the chord passing through the focus and perpendicular to the (main) axis. With a parabola the lactus rectum has always the length 2p. In your case the lactus rectum is 8.
the directriz is below the focus thus the parabola opens upward and the main axis is x = -3.
The midpoint on the main axis between the focus and the directriz is the vertex V(d, c) thus your vertex is V(-3, 3).
The general form of your parabola is:
The distance between focus and directriz is p.
Plug in the values you know:
. Solve for y: