NEW HERE? LEARN MORE
closeclose
Last visit was: 27 Apr 2024, 09:08 It is currently 27 Apr 2024, 09:08
Decision Tracker
My Rewards
New posts
New comers' posts

Close
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
Your Progress

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
Not interested in getting valuable practice questions and articles delivered to your email? No problem, unsubscribe here.
Go to My Error Log Learn more
Close
Request Expert Reply
Confirm Cancel

Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1

User avatar
marcodonzelli
Director
Director
Joined: 22 Nov 2007
Posts: 631
Own Kudos [?]: 2761 [0]
Given Kudos: 0
Send PM
Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   02 Mar 2008, 08:57
Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ?
1. k+b=1
2. k^2 + b^2 =1



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block below for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
User avatar
sreehari
Manager
Manager
Joined: 15 Aug 2007
Posts: 89
Own Kudos [?]: 165 [0]
Given Kudos: 0
Schools:Chicago Booth
Send PM
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   02 Mar 2008, 12:28
Can't believe I spent so much time on this... I am going with E

I couldn't recollect any techniques or tips for tangents to circle, so I went ahead and substituted y=Kx+B in X^2+Y^2=1 in hope to find an intersection point. Then I got X^2*(1+K^2) + 2KBx + B^2 -1 = 0. When tried to see if the roots are real by trying to evaluate b^2 - 4ac, I got to 4K^2-4*B^2+4. And from statement 1 and 2 I couldn't figure if I get a real number or not. So picked E.

I am sure there must be an easy to do this, hope to see some replies here...
User avatar
marcodonzelli
Director
Director
Joined: 22 Nov 2007
Posts: 631
Own Kudos [?]: 2761 [0]
Given Kudos: 0
Send PM
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   02 Mar 2008, 22:54
sreehari wrote:
Can't believe I spent so much time on this... I am going with E

I couldn't recollect any techniques or tips for tangents to circle, so I went ahead and substituted y=Kx+B in X^2+Y^2=1 in hope to find an intersection point. Then I got X^2*(1+K^2) + 2KBx + B^2 -1 = 0. When tried to see if the roots are real by trying to evaluate b^2 - 4ac, I got to 4K^2-4*B^2+4. And from statement 1 and 2 I couldn't figure if I get a real number or not. So picked E.

I am sure there must be an easy to do this, hope to see some replies here...


it is very time-consuming though.

from 1., in case k=1 and b=0 we would have y=x which passes through the origin and is not tangent to the circle.
2. in case k=0 b could be 1 and thus y=1 which touches the circle. anyway it is only one point, since for k=1 and b=0 we have the same situation as in 1.

need quicker ways
User avatar
sreehari
Manager
Manager
Joined: 15 Aug 2007
Posts: 89
Own Kudos [?]: 165 [0]
Given Kudos: 0
Schools:Chicago Booth
Send PM
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   03 Mar 2008, 09:18
Ok.. found something that could be useful

formula to calculate pependicular distance from a point, say (p,q), to a line defined by ax+by+c=0 is

d = (ap+bq+c)/sqrt(a^2+b^2)

plug in (0,0) for (p,q) and 1 for d => B^2-K^2=1

Both statement 1 and 2 cannot be infered from the above equation. So still sticking to E.
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10037 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   17 Mar 2008, 08:34
Expert Reply
E

\(X^2 + Y^2 = 1\) - is a circle that intersects Y-axis in points (0,1), (0,-1) and intersects X-axis in points (1,0), (-1,0).

Consider two edge examples that satisfy both conditions:
k=1; b=0 - y=x does not tangent to circle (intersects it)
k=0; b=1; - y=1 tangents to circle in the point (0,1).

Therefore, E
User avatar
terp26
Current Student
Joined: 22 Oct 2006
Posts: 1212
Own Kudos [?]: 350 [0]
Given Kudos: 12
Schools:Chicago Booth '11
 Q50  V38
Send PM
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   17 Mar 2008, 08:42
Walker , I have come under the assumption that intersect can also be tangent. Is that correct?
User avatar
B
walker
SVP
SVP
Joined: 17 Nov 2007
Posts: 2408
Own Kudos [?]: 10037 [0]
Given Kudos: 361
Concentration: Entrepreneurship, Other
Schools: Chicago (Booth) - Class of 2011
GMAT 1: 750 Q50 V40
Send PM
GMAT ToolKit User
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   17 Mar 2008, 09:49
Expert Reply
terp26 wrote:
Walker , I have come under the assumption that intersect can also be tangent. Is that correct?


https://en.wikipedia.org/wiki/Circle
Attachments

200px-CIRCLE_LINES_2.svg.png
200px-CIRCLE_LINES_2.svg.png [ 14.95 KiB | Viewed 1850 times ]

User avatar
FN
Current Student
Joined: 28 Dec 2004
Posts: 1581
Own Kudos [?]: 642 [0]
Given Kudos: 2
Location: New York City
Concentration: Social Enterprise
Schools:Wharton'11 HBS'12
Send PM
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink] New post   31 Mar 2008, 16:39
I agree its E ..

If either K or B =0

if k=1 then its not tangent

if b=1 then it is tangent..



Archived Topic
Hi there,
This topic has been closed and archived due to inactivity or violation of community quality standards. No more replies are possible here.
Where to now? Join ongoing discussions on thousands of quality questions in our Quantitative Questions Forum
Still interested in this question? Check out the "Best Topics" block above for a better discussion on this exact question, as well as several more related questions.
Thank you for understanding, and happy exploring!
GMAT Club Bot
gmatclubot
Re: Is line Y=KX + B tangent to circle X^2 + Y^2 = 1 ? 1. k+b=1 [#permalink]
31 Mar 2008, 16:39
Moderator:
yashikaaggarwal
Senior Moderator - Masters Forum
3137 posts

Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
Main navigation
GMAT Resources
Partners
MBA Resources
www.gmac.com|www.mba.com | | GMAT Club Rules | Terms and Conditions