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Does the line L intersect the graph of the curve y = x^2 – 6?

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Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 17 Feb 2015, 04:33
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Does the line L intersect the graph of the curve y = x^2 – 6?

(1) The line L passes through the origin and makes an angle of 45o with the positive x-axis.

(2) The line L passes through the point (-2, -2) and (2, 2).

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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 17 Feb 2015, 05:40
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TARGET730 wrote:
Does the line L intersect the graph of the curve y = x^2 – 6?

(1) The line L passes through the origin and makes an angle of 45o with the positive x-axis.

(2) The line L passes through the point (-2, -2) and (2, 2).


The best Method to solve this question will be plotting it graphically

The Graph of y = x^2 - 6 is as follows

The Statement 1 says a line passing through origin at 45 degrees i.e. equation of line y=x which crosses the primary graph at two points as shown in the second picture
Therefore SUFFICIENT


The Statement 2 says a line passing through (-2, -2) and (2, 2) which has equation of line y=x which crosses the primary graph at two points as shown in the second picture
Therefore SUFFICIENT


Answer: Option
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 17 Feb 2015, 07:25
GMATInsight,

Thanks for your quick response.

I am not a quant whiz :( Can you please explain how to draw the graph for the equation y = x^2 - 6 ?
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Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 17 Feb 2015, 07:30
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TARGET730 wrote:
GMATInsight,

Thanks for your quick response.

I am not a quant whiz :( Can you please explain how to draw the graph for the equation y = x^2 - 6 ?


The best ways to draw the graphs is substituting values of x and y

e.g. in Equation y = x^2 - 6

for x = 0, y = -6 [bottom most point of the graph (0, -6)]

for y = 0, x^2 = 6 i.e. x = + \sqrt{6} i.e. x = +2.5 (approx.) [Two points (-2.5, 0) and (2.5, 0)]

Now join the points obtained with free hand and you get the parabola.

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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 17 Feb 2015, 07:38
Great. Thanks much
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 18 Feb 2015, 03:05
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All we need to know is only two points of L or one point and slope. Wa can ignore any information about parabola

St1. Point (0;0) and slope=1. SUFF

St.2. Two points given, so we can count slope. SUFF

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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 19 Feb 2015, 00:33
2
TARGET730 wrote:
Does the line L intersect the graph of the curve y = x^2 – 6?

(1) The line L passes through the origin and makes an angle of 45o with the positive x-axis.

(2) The line L passes through the point (-2, -2) and (2, 2).


Note here that all you need to worry about is getting a unique line. If you have the equation of a line and that of a curve, you will be able to say whether the line intersects the curve or not. The point is that it is not important to figure out whether it actually does intersect because in either case, the information will be sufficient - irrespective of whether the answer is yes or no. So actually drawing the curve and the line is not required.

Both statements individually give you a distinct line. So you will be able to say whether the line intersects the curve or not.

Answer (D)

This brings up an interesting question - given the equation of the curve y = x^2 – 6, what kind of lines will not intersect it? Think about it.
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 19 Feb 2015, 00:41
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TARGET730 wrote:
GMATInsight,

Thanks for your quick response.

I am not a quant whiz :( Can you please explain how to draw the graph for the equation y = x^2 - 6 ?


It will be great if you learn how to quickly draw and manipulate graphs of lines and some curves such as circle and parabola.

These two posts teach you how to draw the graphs of lines intuitively from equations:

http://www.veritasprep.com/blog/2010/12 ... he-graphs/
http://www.veritasprep.com/blog/2010/12 ... s-part-ii/

You can follow the same approach with curves if you know some basic shapes such as y = x^2 is an upward opening parabola centered at (0, 0).
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 19 Feb 2015, 01:00
Thank you Karishma
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Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 10 Apr 2019, 23:00
I solved the question by assuming that both the statements mentioned tells us about that line passes through origin.
And then solved the equation of parabola and checking whether discriminant equals to zero or not.

Since it is not equals to zero it will not intersect.

Please help and correct me, as i am new to this topic and getting confused while solving Coordinate Geometry Questions.
Also, if someone can share some study material on coordinate geometry
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?  [#permalink]

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New post 11 Apr 2019, 02:40
anmolgmat14 wrote:
I solved the question by assuming that both the statements mentioned tells us about that line passes through origin.
And then solved the equation of parabola and checking whether discriminant equals to zero or not.

Since it is not equals to zero it will not intersect.

Please help and correct me, as i am new to this topic and getting confused while solving Coordinate Geometry Questions.
Also, if someone can share some study material on coordinate geometry



I am not sure what you mean by solving the equation of parabola. It is already given to you. Do you mean you found the equation of the line and then solved with the equation of parabola to see if they intersect? As I mentioned earlier, solving to find the points of intersection is useless. As long as we get unique equations for line and parabola, we CAN find and answer. Hence it WILL be sufficient.

Check out our blog here for posts on co-ordinate geometry:
https://www.veritasprep.com/blog/catego ... coordinate
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Re: Does the line L intersect the graph of the curve y = x^2 – 6?   [#permalink] 11 Apr 2019, 02:40
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