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# At how many points does the parabola y = 1/2*x^2 intersect the hyperbo

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Math Expert
Joined: 02 Sep 2009
Posts: 51218
At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 00:47
00:00

Difficulty:

75% (hard)

Question Stats:

50% (01:20) correct 50% (01:25) wrong based on 178 sessions

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At how many points does the parabola y = 1/2*x^2 intersect the hyperbola x^2 – y^2 = 1?

A. 0
B. 1
C. 2
D. 3
E. 4

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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 01:01
4
5
Bunuel wrote:
At how many points does the parabola y = 1/2*x^2 intersect the hyperbola x^2 – y^2 = 1?

A. 0
B. 1
C. 2
D. 3
E. 4

Second method to solve the question is to find the solutions algebraically
Given,
Parabola y = 1/2*x^2 i.e. x^2 = 2y

Hyperbola x^2 – y^2 = 1

Substitute the value of x^2 from equation of parabola to equation of Hyperbola

x^2 – y^2 = 1
i.e. (2y) – y^2 = 1
i.e. y^2 - 2y + 1 = 0
i.e. (y-1)^2 = 0
i.e. y = 1
Substituting the value of y to fin the value of x
x^2 = 2*1=2
i.e. x = +$$\sqrt{2}$$

Hence, 2 points of Intersections

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##### General Discussion
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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 00:52
Are you sure such questions can come I forgot what does a parabola look like

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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 00:53
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

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At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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Updated on: 22 Feb 2017, 01:01
Bunuel wrote:
At how many points does the parabola y = 1/2*x^2 intersect the hyperbola x^2 – y^2 = 1?

A. 0
B. 1
C. 2
D. 3
E. 4

Parabola y = 1/2*x^2

Hyperbola x^2 – y^2 = 1

The best method is to draw the figure...

The figure shows that total points of intersections are two in number

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Originally posted by GMATinsight on 22 Feb 2017, 00:55.
Last edited by GMATinsight on 22 Feb 2017, 01:01, edited 1 time in total.
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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 01:03
nailin16 wrote:
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

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Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.
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At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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22 Feb 2017, 17:24
1
GMATinsight wrote:
nailin16 wrote:
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

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Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.

Yes, that's true, but consider: Do you really need to know anything about *either* parabolas or hyperbolas or what they look like to solve this problem?

See, for instance, your own second solution.
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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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16 Jun 2017, 22:15
AnthonyRitz wrote:
GMATinsight wrote:
nailin16 wrote:
Are you sure such questions can come I forgot what does a parabola or hyperbole look like

Sent from my SM-G600FY using GMAT Club Forum mobile app

Hi @nalin16,

You are right about your apprehension. Parabola has been witnessed in GMAT however no incidence of Hyperbola has been witnessed so far so I also feel that that hyperbola can not be part of any question of GMAT yet.

Yes, that's true, but consider: Do you really need to know anything about *either* parabolas or hyperbolas or what they look like to solve this problem?

See, for instance, your own second solution.

No, you don't necessarily need to know what a parabola or hyperbola looks like- you just need to know how to effectively substitute the parabola in the hyperbola so as to derive points of intersection. Simple, intersection of hyperbola and parabola= substitute parabola into hyperbola. Now, you can also substitute for the x values- the GMAT just makes a bit more difficult to figure out which is faster and more effective to substitute.
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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

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25 Nov 2018, 16:50
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Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo &nbs [#permalink] 25 Nov 2018, 16:50
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