SOLUTION: If the vertex is at the Origin write the equation of the parabola and identify the directrix 4. Focus at (0, 1) 5. Focus at (0, 5) focus 6. directrix y = 7 7. di

Question 840671: If the vertex is at the Origin write the equation of the parabola and identify the
directrix
4. Focus at (0, 1)
5. Focus at (0, 5)
focus
6. directrix y = 7
7. directrix y = -3
I am so lost it is unreal.... How do I do this? I have spent 3 hours looking for an example at the least with nothing found...
Answer by lwsshak3(11628) (Show Source): You can put this solution on YOUR website!
If the vertex is at the Origin write the equation of the parabola and identify the directrix
4. Focus at (0, 1)
parabola opens upward:
axis of symmetry:x=0 or y-axis
basic form of equation: x^2=4py
p=1(distance from vertex to given focus on the axis of symmetry)
4p=4
equation; x^2=4y
directrix: y=-1(p-distance from vertex to directrix on the axis of symmetry)
..
5. Focus at (0, 5)
parabola opens upward:
axis of symmetry:x=0 or y-axis
basic form of equation: x^2=4py
p=5(distance from vertex to given focus on the axis of symmetry)
4p=20
equation; x^2=20y
directrix: y=-5(p-distance from vertex to directrix on the axis of symmetry)
..
6. directrix y = 7
parabola opens downward:
axis of symmetry:x=0 or y-axis
basic form of equation: x^2=-4py
p=7(distance from vertex to given directrix on the axis of symmetry)
4p=28
equation; x^2=-28y
focus: y=(0,-7)(p-distance from vertex to focus on the axis of symmetry)
..
7. directrix y = -3
parabola opens upward:
axis of symmetry:x=0 or y-axis
basic form of equation: x^2=4py
p=3(distance from vertex to given directrix on the axis of symmetry)
4p=12
equation; x^2=12y
focus: y=(0,-3)(p-distance from vertex to focus on the axis of symmetry)
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