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Finding the vertex, focus, and directrix of the parabola

1. 20x=y2
2. (x-3)squared =1/2(y+1)
3. y2+14y+4x+45=0

Find an equation of the parabola that satisfies the given conditions
Focus F(0-4), directrix y=4

Find the vertices, the foci and the equations of the asymptotes of the hyperbola.
1.y2divided by 49 minus x2 divided by sixteen =1
2.x2-2y2=8
Find an equation fot the hyperbola that has its center as the origin and satisfies the given conditions
1.Foci F(plus/minus 8,0) vertices V(plus/minus5,0)

Find the vertices and foci of the ellipse.
1. x2 divided by 25 + y2 divided by 16 =1
2. (x+2)2 divided by 25 + (y-3)squared divided by 4 =1

Find an equation for the ellipse that has its center at the origin and satisfies the given conditions.

1. Vertices V(0, plus/minus5), minus axis of length 3

Solution Preview

Standard forms of the parabola are
<br>y = x^2/4P parabola opens up
<br>y = -x^2/4P parabola opens down
<br>x = y^2/4p parabola opens right and
<br>x^2= -y^2/4p shows a parabola opens left
<br>
<br>For parabolas opening up/down, the directrix is a horizontal line in the form y = + p
<br>For parabolas opening right/left, the directrix is a vertical line in the form x = + p
<br>The vertex point for all of the above is (0,0)
<br>
<br>For parabolas opening up/down, the directrix is a horizontal line in the form y = + p. For parabolas ...

Solution Summary

The problem is solved giving all necessary mathematical steps. It will enable you to do similar problems yourself.

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