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Coordinate geometry parabola

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by vipulgoyal » Fri Jul 03, 2015 1:22 am
The line represented by which of the following equations does not interact with the line represented by
Y=3x^2 +5x +1
A) Y=2x^2 +5x +1
B) Y= x^2 +5x +2
C) Y=3x^2 +5x +2
D) Y=3x^2 +7x +2
E) Y=x^2 +7x +1

C
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Source: — Data Sufficiency |
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by theCEO » Fri Jul 03, 2015 7:41 am
vipulgoyal wrote:The line represented by which of the following equations does not interact with the line represented by
Y=3x^2 +5x +1
A) Y=2x^2 +5x +1
B) Y= x^2 +5x +2
C) Y=3x^2 +5x +2
D) Y=3x^2 +7x +2
E) Y=x^2 +7x +1

C
2 lines will only interact if they share at similar point.
To test if they intersect, we should set both lines to be equal
If we give a solution, then the lines intesect
If we don't get a solution, the lines do not interact

A)
Y=2x^2 +5x +1 = 3x^2 +5x +1
0 = x^2 + x --> we can solve for a solution, therfore line intersects

B)
Y= x^2 +5x +2 = 3x^2 +5x +1
0 = 2x^2 -1 --> we can solve for a solution, therfore line intersects

C)
Y=3x^2 +5x +2 = 3x^2 +5x +1
2 = 1 --> impossible, there is no solution, therefore lines do not intersects, we can stop here :)

D)
Y=3x^2 +7x +2 = 3x^2 +5x +1
0 = -2x -1 --> we can solve for a solution, therfore line intersects

E)
Y=x^2 +7x +1 = 3x^2 +5x +1
0 = 2x^2 -2x --> we can solve for a solution, therfore line intersects

ans = c
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