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# Do lines y =ax^2 +b and y =cx^2+d cross? A:a = -c B:b>d

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Manager
Joined: 09 Oct 2008
Posts: 93
Do lines y =ax^2 +b and y =cx^2+d cross? A:a = -c B:b>d [#permalink]

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21 Oct 2008, 20:44
Do lines y =ax^2 +b and y =cx^2+d cross?

A:a = -c
B:b>d

how to solve this kind of questions? what is m for both lines as we have x^2 in line equation.?what is condition to check that line are crossing each other or not?

Thanks

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SVP
Joined: 29 Aug 2007
Posts: 2426

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21 Oct 2008, 21:31
vishalgc wrote:
Do lines y =ax^2 +b and y =cx^2+d cross?

A:a = -c
B:b>d

how to solve this kind of questions? what is m for both lines as we have x^2 in line equation.?what is condition to check that line are crossing each other or not?

Thanks

m for first line = ax
m for second line = cx = - ax

A: nsf. if a is not 0 (hence c = 0), the lines intersect. if a is 0 (hence c = 0), the does not intersect. i am assuming overlapiing is not intersection.
B: b>d doesnot tell anything.

A+B: also not suff. b and d have nothing to do with slopes and intersection. only slope determines the intersection.

so E.
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VP
Joined: 17 Jun 2008
Posts: 1479

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22 Oct 2008, 00:20
Not sure whether my approach is correct.

If the two lines intersect, the x and y co-ordinates will be the same from the two lines of the point of intersection.

Hence, ax^2 + b = cx^2 + d
or (c-a)x^2 = b-d
or x^2 = (b-d)/2c.

Now, for real values of x, (b-d)/2c has to be +ve. We know from stmt2 that (b-d) > 0, but still not sure whether c is +ve.

Hence, E.
VP
Joined: 05 Jul 2008
Posts: 1340

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22 Oct 2008, 09:45
These equations are NOT lines. Are they ??

line is y=mx+b and the given equations appear to be a parabola??
Senior Manager
Joined: 29 Mar 2008
Posts: 341

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22 Oct 2008, 12:12
vishalgc wrote:
Do lines y =ax^2 +b and y =cx^2+d cross?

A:a = -c
B:b>d

how to solve this kind of questions? what is m for both lines as we have x^2 in line equation.?what is condition to check that line are crossing each other or not?

Thanks

If the question stem is - Do lines y =ax +b and y = cx+d cross?
Then it is (A), m1*m2 = -1 which means that the two lines are perpendicular and hence cross.

Is this question correct with x^2?

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Re: line: y=ax^2+b   [#permalink] 22 Oct 2008, 12:12
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# Do lines y =ax^2 +b and y =cx^2+d cross? A:a = -c B:b>d

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