SOLUTION: Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2. choices below y2 = 2x y = one divided by two x2 y2 = 8x

Algebra ->  Trigonometry-basics -> SOLUTION: Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2. choices below y2 = 2x y = one divided by two x2 y2 = 8x       Log On


   



Question 1135979: Find the standard form of the equation of the parabola with a focus at (0, 2) and a directrix at y = -2.
choices below
y2 = 2x

y = one divided by two x2

y2 = 8x

y = one divided by eight x2

Answer by MathLover1(20850) About Me  (Show Source):
You can put this solution on YOUR website!
given: a focus at (0, 2) and a directrix at y+=+-2

the vertex, exactly between the focus and directrix, must be at (h, k) = (0, 0)
the absolute value of p+is the distance between the vertex and the focus and the distance between the vertex and the directrix. (The sign on p tells me which way the parabola faces.) Since the focus and directrix are 2 units apart, then this distance has to be one unit, so abs%28p+%29+=2
Since this is a "upward" parabola, then the x part gets squared, rather than the y part. So the conics form of the equation must be:
4p%28y-+y%5B1%5D%29+=+%28x+-x%5B1%5D%29%5E2
4%2A2%28y-+0%29+=+%28x+-0%29%5E2
8y=+x%5E2
y=%281%2F8%29x%5E2+