Question 432734: Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line.
2.F(0,-1), y =1
4.F(0,-8), y = 8
6.F(1/2,0), x = -1/2
Answer by lwsshak3(11628)   (Show Source):
You can put this solution on YOUR website! Write an equation for a graph that is the set of all points in the plane that are equidistant from the given point and the given line.
2.F(0,-1), y =1
4.F(0,-8), y = 8
6.F(1/2,0), x = -1/2
..
The given problem is the definition of a parabola. The given point is the focus and the line is called the directrix. There are four forms with horizontal or vertical axis of symmetry:
x^2=+-4py(parabola opens up and down)
y^2=+-4px(parabola opens right and left)
..
2.F(0,-1), y =1
p=1, directrix y=1, parabola opens downward
Equation: x^2=-4y
..
4.F(0,-8), y = 8
p=8,directrix y=8, parabola opens downward
Equation: x^2=-32y
..
6.F(1/2,0), x = -1/2
p=1/2,directrix y=-1/2, parabola opens rightward
Equation: y^2=2x
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