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Do lines y = ax^2 + b and y = cx^2 + d cross? 1. a = -c 2. b

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Do lines y = ax^2 + b and y = cx^2 + d cross? 1. a = -c 2. b [#permalink] New post 20 Oct 2007, 19:16
Do lines y = ax^2 + b and y = cx^2 + d cross?

1. a = -c
2. b > d
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Re: coordinate geometry [#permalink] New post 20 Oct 2007, 19:23
beckee529 wrote:
Do lines y = ax^2 + b and y = cx^2 + d cross?

1. a = -c
2. b > d


A. since the slopes are -ve reciprocle. the lines are perpendicular to each other.............................

if b>d, the lines could be parallel or not.
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 [#permalink] New post 20 Oct 2007, 19:35
i also picked A but that is not the answer
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 [#permalink] New post 20 Oct 2007, 20:17
I get C..

1) insuff cus ok so we know that both curves are opposite each other but we dont know the intersection

2) insuff again we dont know if the curves are opposite or not

together sufficient..
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 [#permalink] New post 20 Oct 2007, 20:30
this one is quite tricky.. anyone else?





oa is E
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Re: coordinate geometry [#permalink] New post 20 Oct 2007, 20:45
beckee529 wrote:

Do lines y = ax^2 + b and y = cx^2 + d cross?

1. a = -c
2. b > d


A line is of the form y=mx+c

y = ax*x + b (here slope is ax)

y = cx*x + d(here slope is cx)

From(A) a = -c ( doest mean they are perpendicular or even parallel for that matter)

For perpendicular product of slopes should be -1 which is not here
For parallel lines only the y-intercept should be different which is not here again.

So A is correct

Coming to (II) b>d doesnt give a clue about intersection of these lines

Hence A should be it (unless I am missing something)

**************************************************
Its not A...I made a mistake here


It should be E here

suppose a=1 and c=-1 in (I) and x=1 too then they are perpendicular lines..But we are no tsure of the values

Hence E

Very good question indeed
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Re: coordinate geometry [#permalink] New post 20 Oct 2007, 22:51
trivikram wrote:
beckee529 wrote:

Do lines y = ax^2 + b and y = cx^2 + d cross?

1. a = -c
2. b > d


A line is of the form y=mx+c

y = ax*x + b (here slope is ax)

y = cx*x + d(here slope is cx)

From(A) a = -c ( doest mean they are perpendicular or even parallel for that matter)

For perpendicular product of slopes should be -1 which is not here
For parallel lines only the y-intercept should be different which is not here again.

So A is correct

Coming to (II) b>d doesnt give a clue about intersection of these lines

Hence A should be it (unless I am missing something)

**************************************************
Its not A...I made a mistake here


It should be E here

suppose a=1 and c=-1 in (I) and x=1 too then they are perpendicular lines..But we are no tsure of the values

Hence E

Very good question indeed

not convinced with E.

Following your post: slope of line y = ax^2 + b is ax and line y = cx^2 + d is cx.

no matter the value of x, if a = -c, ax and cx has inverse relation of -1. so A should be sufficient to answer.

I still stick with A and am not convinced with E.
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 [#permalink] New post 20 Oct 2007, 23:22
here is the OE folks:

S1 + S2 is not sufficient. Consider y = -x2 + 1 , y = x2 + 0 (the answer is YES) and y = x2 + 1 , y = -x2 + 0 (the answer is NO).
The correct answer is E.

i'm up for any open discussion! :)
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 [#permalink] New post 21 Oct 2007, 00:20
(E) it is :)

A line does not have to be straight ;)... Here, we are with the example, it's 2 curves that we are speaking about.

The best way here is to draw XY planes.

We have:
o y = ax^2 + b
o y = cx^2 + d

A first thing to know, when we have such form of curves (no t*x involved), a curve is simetrical to the Y-axis, reaching an extremum at x=0.

A second thing is that a and c have a direct impact on the widths of the curves and on the shape of them : "valleys" or "mountains".

Now, let us go in the statments.

Stat1
a=-c.... Implies a similar width but a different shape. The one that is positive represents a valley and so the other that is negatize creates a montain.

All depend on the values of b and d to intersect.

o If b=d, we have a single point of intersection on the Y axis.

o If b > d, we have 2 cases :
- a > c : the 2 curves have no intersection and as the line X Axis as an axis of symetry
- a < c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry

o If b < d, we have 2 cases :
- a > c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry
- a < c : the 2 curves have no intersection and as the line X Axis as an axis of symetry

INSUFF.

Stat2
b > d.

This just says that the 2 extremum of the 2 curves are situated one above the other one.

That's not giving informations on:
- the width of the cuvres : 1 valley with a smaller width could be contained in 1 valley with a larger width
- the shapes of the curves: 2 valleys, 1 mountain and 1 valley or 2 mountains

INSUFF.

Both 1 and 2
We are left with the 2 cases as a=-c:

b > d :
- a > c : the 2 curves have no intersection and as the line X Axis as an axis of symetry
- a < c : the 2 curves have 2 intersections (symetrical to the Y axis) and as the line X Axis as an axis of symetry

INSUFF.
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 [#permalink] New post 21 Oct 2007, 06:52
thanks fig.. that makes a whole lot more sense now! learn something new from gmatclub ;)
  [#permalink] 21 Oct 2007, 06:52
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Do lines y = ax^2 + b and y = cx^2 + d cross? 1. a = -c 2. b

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