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.

1. State the key features (vertex,focus,directrix, direction of opening, and axis of symmetry) of each parabola, and sketch the graph.
a) ysquared-2x+4y-7=0
2. Find the equation of each parabola.
a) parabola with focus (-2,-1) anddirectrix y=5
b) ysquared=-6x translated according to ((x,y)arrow(x-2, y+4)

1. Find the equation of a parabola whose vertex is (0,0) anddirectrix is the line y=3.
2. Find thevertex,focus,anddirectrix of (x-2)^2=12(y+1). Find the latus rectum and graph theparabola, making sure that all points and axis are labeled.
3. Find the equation of the ellipse whose center is the origin and has a

1.) Find thevertex, focus , directrix of theparabolaand sketch its graph
y+ 12x - 2x^2 = 16
2.) Sketch the curve by using parametric equations to plot points. Indicate with an arrow the direction in which the curve is traced as t increases
x= 2 cos t, y= t- cos t, (0 (

Harry has $2.25 in Nickels, Dimes and quarters. If he had twice as many nicels, half as many dimes ....
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Find theVertex, Focus and ...
Find the equation of theparabola ....
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Find theVertex, Foc

1-Find the vertex focus,and directrex of theparabola=
1-x2= 2 (x+y)
2-Write an equation of the vertical parabola that contains (-1,2) with focus (3,1) and which opens upward.
3-Write an equation for theparabola that has vertex (1,2) and its axis is parallel to the x-axis, passes through the point (13,4)
4-Find all e