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In xy plane, a certain line L1 has how many intersections

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In xy plane, a certain line L1 has how many intersections  [#permalink]

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New post Updated on: 03 Oct 2012, 03:59
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In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

(1) Line L1 does not intersect the X- Axis
(2) The point Q (2,1) lies on line L1

Originally posted by shivanigs on 03 Oct 2012, 00:25.
Last edited by Bunuel on 03 Oct 2012, 03:59, edited 1 time in total.
Renamed the topic and edited the question.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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New post 03 Oct 2012, 04:20
6
8
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

Probably the best way to deal with this question is to make diagrams.

(1) Line L1 does not intersect the X- Axis. This statement implies that line L1 is parallel to x-axis. We can have 0, 1, or 2 intersection points:
Attachment:
Parabola.png
Parabola.png [ 10.82 KiB | Viewed 6774 times ]
Not sufficient.

(2) The point Q (2,1) lies on line L1. Again, we can have 0, 1, or 2 intersection points:
Attachment:
Parabola2.png
Parabola2.png [ 10.18 KiB | Viewed 6774 times ]
Not sufficient.

(1)+(2) Line L1 is parallel to x-axis and passes through the point (2, 1):
Attachment:
Parabola3.png
Parabola3.png [ 10.83 KiB | Viewed 6767 times ]
As we can see the line does not intersect the parabola. Sufficient.

Answer: C.

Hope it's clear.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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New post Updated on: 03 Oct 2012, 06:26
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 0 ,1 or two points.

STAT1 and STAT2 combined we have:
y=1 as the equation of the line. So we have 0 points of intersection.

So, answer will be C
Hope it helps!
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Originally posted by BrushMyQuant on 03 Oct 2012, 00:38.
Last edited by BrushMyQuant on 03 Oct 2012, 06:26, edited 1 time in total.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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New post 03 Oct 2012, 04:23
nktdotgupta wrote:
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 1 or two points.

STAT1 and STAT2 combined we have:
y=2 as the equation of the line. So we have only one point of intersection which is (0,2)

So, answer will be C
Hope it helps!


Check the solution above. Your answer is correct but some parts of the solution are not.
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Re: In xy plane, a certain line L1 has how many intersections wi  [#permalink]

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New post 03 Oct 2012, 06:26
Bunuel wrote:
nktdotgupta wrote:
In xy plane, a certain line L1 has how many intersections with y = x^2 +2?

1. Line L1 does not intersect the X- Axis
2. The point Q (2,1) lies on line L1

STAT1
tells us that the line is parallel to x axis. So the equation of the line will be y = k (where k is a constant)
For every value of:
k >2 we have two point of intersections. (x^2= k -2 will give two values of x)
For k =2 we have one point of intersection only point of intersection is (0,2)
and for k < 2 we Dont have any point of intersection (x^2= -ve, which is not possible)

So, 1 is insufficient

STAT2:
Statement2 by itself is nOt sufficient as we do not know the equation of the line. the line can intersect the given curve at 1 or two points.

STAT1 and STAT2 combined we have:
y=2 as the equation of the line. So we have only one point of intersection which is (0,2)

So, answer will be C
Hope it helps!


Check the solution above. Your answer is correct but some parts of the solution are not.


@Bunuel: Thanks.. edited.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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New post 03 Oct 2012, 14:22
bunuel, very well drawn picture .
difficult problem very easily solved.
thanks a lot.
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coordinate geometery  [#permalink]

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New post 12 Oct 2014, 06:19
IN the XY Plane, a certain line L has how many intersections with y=x^2+2 ?
1. Line L doesn't intersect x-axis.
2. The point Q(2,1) lies on line L
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Re: coordinate geometery  [#permalink]

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New post 12 Oct 2014, 06:37
1. Line L doesn't intersect x-axis.
Line L is parallel to x axis. But no information on point of intersection with y=x^2+2.
Statement not sufficient.

2. The point Q(2,1) lies on line L
Again statement is not sufficient to determine point of intersection with y=x^2+2.

1+2,
Line L is parallel to x axis and passes through point Q(2,1). Minimum value of y coordinate for y=x^2+2 is 2 when x=0.
As absolute value of x increases, value of y coordinate also increases. Hence Line L has no intersection point with y=x^2+2.

Hence combined statements are sufficient.
Ans= C

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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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New post 12 Oct 2014, 07:47
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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New post 15 Dec 2015, 19:27
the equation given is a parabola, open upwards, the lowest point is at 0,2.
now, the first statement doesn't tell much, except that it is a parallel line to x-axis, only in the case of parallel to x-axis the line never intersects the x-axis. it might be the case that the line intersects the line at 0, 1, or 2 points. not sufficient.

statement two, says that it intersects at point 1,2. doesn't tell much. might be only 1 point, or more points, depending on the equation of the line.

1+2 says that line L1 is a parallel line, and it doesn't intersect the parabola at all. this one is sufficient to give a definitive answer.
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Re: In xy plane, a certain line L1 has how many intersections  [#permalink]

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Re: In xy plane, a certain line L1 has how many intersections   [#permalink] 09 Apr 2019, 12:33
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