Question 800858: State the coordinates of the focus and the equation of the directrix of the parabola defined defined by each equation
a) y^2 = 4x
b) x^2 = 8y
Can you please help me out, thanks so much in advance:)
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! State the coordinates of the focus and the equation of the directrix of the parabola defined defined by each equation
a) y^2 = 4x
b) x^2 = 8y
**
There are 4 basic forms of equation for parabolas with vertices at (0,0)
x^2=4py (Parabola opens up)
x^2=-4py (Parabola opens down)
y^2=4px (Parabola opens right)
y^2=-4px (Parabola opens up)
..
a) y^2 = 4x(Parabola opens right)
axis of symmetry:y=0 or x-axis
4p=4
p=1
directrix: x=-1 (p-distance to left of vertex on the axis of symmetry)
Focus:(1,0)(p-distance to right of vertex on the axis of symmetry)
..
b) x^2 = 8y (Parabola opens up)
axis of symmetry:x=0 or y-axis
4p=8
p=2
directrix: y=-2 (p-distance below vertex on the axis of symmetry)
Focus:(0,2)(p-distance above vertex on the axis of symmetry)
..
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