It is currently 21 Oct 2017, 03:30

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

Events & Promotions

Events & Promotions in June
Open Detailed Calendar

What is the least possible distance between a point on the

Author Message
Manager
Joined: 20 Jan 2011
Posts: 63

Kudos [?]: 1 [0], given: 8

Show Tags

24 Apr 2011, 11:51
Tough question, takes more than 2 min

Kudos [?]: 1 [0], given: 8

Manager
Joined: 04 Oct 2013
Posts: 162

Kudos [?]: 119 [0], given: 55

Location: India
GMAT Date: 05-23-2015
GPA: 3.45
Re: What is the least possible distance between a point on the [#permalink]

Show Tags

01 May 2014, 07:55
What is the least possible distance between a point on the circle $$x^2 + y^2 = 1$$ and a point on the line $$y = \frac{3}{4}x - 3$$ ?

(A) 1.4
(B) $$\sqrt{2}$$
(C) 1.7
(D) $$\sqrt{3}$$
(E) 2.0

Clearly, the required point on the circle, which is at least distance from the given line satisfies not only the equation of the given circle that has center at origin but also the equation of the line that is perpendicular to the given line.

The equation of the line passing through (0,0) and perpendicular to the given line $$y = \frac{3}{4}x - 3$$ is $$y =- \frac{4}{3}x$$

Since, the co-ordinate of the required point satisfies equation of the circle with unit radius, substituting, $$y =- \frac{4}{3}x$$ in equation $$x^2 + y^2=1$$, we obtain $$x = \frac{3}{5}$$and $$y = \frac{-4}{5}$$

The distance of the required point ( 3/5, - 4/5) from the line $$y = \frac{3}{4}x - 3$$ or $$4y - 3x + 12 =0$$

=$$|(-3)(3/5) + 4(-4/5) +12 |/ \sqrt{(4^2 +(-3)^2)}$$ = $$\frac{7}{5}$$ or, 1.4

Attachments

Least-Distance-of-A-Point-On-Circle.docx [29.11 KiB]

Kudos [?]: 119 [0], given: 55

Re: What is the least possible distance between a point on the   [#permalink] 01 May 2014, 07:55

Go to page   Previous    1   2   3   [ 42 posts ]

Display posts from previous: Sort by

What is the least possible distance between a point on the

Moderator: Bunuel

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne Kindly note that the GMAT® test is a registered trademark of the Graduate Management Admission Council®, and this site has neither been reviewed nor endorsed by GMAC®.