GMAT Question of the Day - Daily to your Mailbox; hard ones only

 It is currently 22 Sep 2019, 18:22

### GMAT Club Daily Prep

#### Thank you for using the timer - this advanced tool can estimate your performance and suggest more practice questions. We have subscribed you to Daily Prep Questions via email.

Customized
for You

we will pick new questions that match your level based on your Timer History

Track

every week, we’ll send you an estimated GMAT score based on your performance

Practice
Pays

we will pick new questions that match your level based on your Timer History

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

Author Message
TAGS:

### Hide Tags

Math Expert
Joined: 02 Sep 2009
Posts: 58098
At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 01:47
00:00

Difficulty:

65% (hard)

Question Stats:

52% (01:39) correct 48% (01:39) wrong based on 214 sessions

### HideShow timer Statistics

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

_________________
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 02:01
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

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
##### General Discussion
Veritas Prep GMAT Instructor
Affiliations: Veritas Prep
Joined: 21 Dec 2014
Posts: 45
Location: United States (DC)
GMAT 1: 790 Q51 V51
GRE 1: Q800 V800
GPA: 3.11
WE: Education (Education)
At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 18:24
1
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.
Manager
Joined: 05 Apr 2014
Posts: 138
Location: India
Schools: ISB '19, Fox"19
GMAT 1: 660 Q48 V33
GPA: 3
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 01:52
Are you sure such questions can come I forgot what does a parabola look like

Sent from my SM-G600FY using GMAT Club Forum mobile app
Manager
Joined: 05 Apr 2014
Posts: 138
Location: India
Schools: ISB '19, Fox"19
GMAT 1: 660 Q48 V33
GPA: 3
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 01:53
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
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

Updated on: 22 Feb 2017, 02:01
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

Attachments

File comment: www.GMATinsight.com

123456.jpg [ 103.06 KiB | Viewed 2032 times ]

_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION

Originally posted by GMATinsight on 22 Feb 2017, 01:55.
Last edited by GMATinsight on 22 Feb 2017, 02:01, edited 1 time in total.
CEO
Status: GMATINSIGHT Tutor
Joined: 08 Jul 2010
Posts: 2972
Location: India
GMAT: INSIGHT
Schools: Darden '21
WE: Education (Education)
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

22 Feb 2017, 02:03
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.
_________________
Prosper!!!
GMATinsight
Bhoopendra Singh and Dr.Sushma Jha
e-mail: info@GMATinsight.com I Call us : +91-9999687183 / 9891333772
Online One-on-One Skype based classes and Classroom Coaching in South and West Delhi
http://www.GMATinsight.com/testimonials.html

ACCESS FREE GMAT TESTS HERE:22 ONLINE FREE (FULL LENGTH) GMAT CAT (PRACTICE TESTS) LINK COLLECTION
Director
Joined: 12 Nov 2016
Posts: 704
Location: United States
Schools: Yale '18
GMAT 1: 650 Q43 V37
GRE 1: Q157 V158
GPA: 2.66
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

16 Jun 2017, 23:15
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.
Non-Human User
Joined: 09 Sep 2013
Posts: 12523
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo  [#permalink]

### Show Tags

25 Nov 2018, 17:50
Hello from the GMAT Club BumpBot!

Thanks to another GMAT Club member, I have just discovered this valuable topic, yet it had no discussion for over a year. I am now bumping it up - doing my job. I think you may find it valuable (esp those replies with Kudos).

Want to see all other topics I dig out? Follow me (click follow button on profile). You will receive a summary of all topics I bump in your profile area as well as via email.
_________________
Re: At how many points does the parabola y = 1/2*x^2 intersect the hyperbo   [#permalink] 25 Nov 2018, 17:50
Display posts from previous: Sort by