SOLUTION: What is the equation in standard form for the parabola with vertex (0,0) and directrix you= -4

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Question 1075737: What is the equation in standard form for the parabola with vertex (0,0) and directrix you= -4
Answer by josmiceli(19441) About Me  (Show Source):
You can put this solution on YOUR website!
If the form of the equation is
+y+=+a%2Ax%5E2+%2B+bx+%2B+c+, then the
x-value of the vertex is at +-b%2F%282a%29+
Since the vertex is (0,0), then
+-b%2F%282a%29+=+0+ and
+b+=+0+
+y+=+a%2Ax%5E2+%2B+c+
and
+y+=+a%2A0+%2B+c+
+y+=+c+
and since the vertex is at (0,0)
+c+=+0+
So far I have:
+y+=+a%2Ax%5E2+
------------------
Let the y-value of the focus = +f+
+%28+f+%2B+%28-4%29+%29+%2F+2+=+0+
+f+-+4+=+0+
+f+=+4+
The x-value of the focus will be the same as the vertex,
so the focus is at ( 0,4 )
-----------------------------------
According to the formula, a parabola with focus ( x[f], y[f] )
and directrix +y+=+d+ has the form
+%28+x+-+x%5Bf%5D+%29%5E2+%2B+y%5Bf%5D%5E2+-+d%5E2+=+2%2A%28+y%5Bf%5D+-+d+%29%2Ay+
+%28+x+-+0+%29%5E2+%2B+4%5E2+-+%28-4%29%5E2+=+2%2A%28+4+-%28-4%29+%29%2Ay+%7D+
+x%5E2+%2B+16+-+16+=+2%2A8%2Ay+
+16y+=+x%5E2+
+y+=+%281%2F16%29%2Ax%5E2+