SOLUTION: Find an equation for the parabola that has its vertex at the origin and satisfies the given condition. Directrix y = 1/6

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Question 1170439: Find an equation for the parabola that has its vertex at the origin and satisfies the given condition.
Directrix y = 1/6


Answer by MathLover1(20849) About Me  (Show Source):
You can put this solution on YOUR website!
given:
the parabola that has its vertex at the origin => (h,k)=(0,0)
and that directrix y+=+1%2F6
The standard form is %28x+-+h%29%5E2+=+4p+%28y+-+k%29, where the focus is (h, k+%2B+p) and the directrix is y+=+k+-+p. If the parabola is rotated so that its vertex is (h,k) and its axis of symmetry is parallel to the x-axis, it has an equation of %28y+-+k%29%5E2+=+4p+%28x+-+h%29, where the focus is (h+%2B+p, k) and the directrix is x+=+h+-+p}
so. use %28x+-+h%29%5E2+=+4p+%28y+-+k%29
%28x+-+0%29%5E2+=+4p+%28y+-+0%29
x%5E2+=+4p+%2Ay+
y=x%5E2+%2F4p+
since directrix y+=+1%2F6, the directrix is y+=+k+-+p, and k=0, we have
1%2F6+=+0+-+p
p+=++-+1%2F6

y=x%5E2+%2F%284%28-+1%2F6%29%29+
y=x%5E2+%2F%28-4%2F6%29+
y=x%5E2+%2F%28-2%2F3%29+
y=%28-3%2F2%29+x%5E2+-> your answer

the focus is (h, k+%2B+p) =(0, -+1%2F6)