GMAT Question of the Day: Daily via email | Daily via Instagram New to GMAT Club? Watch this Video

 It is currently 07 Aug 2020, 10:27

### 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

# What is the least possible distance between a point on the circle x^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics
Author Message
TAGS:

### Hide Tags

CEO
Joined: 20 Mar 2014
Posts: 2525
Concentration: Finance, Strategy
Schools: Kellogg '18 (M)
GMAT 1: 750 Q49 V44
GPA: 3.7
WE: Engineering (Aerospace and Defense)
Re: What is the least possible distance between a point on the circle x^2  [#permalink]

### Show Tags

27 Jul 2015, 12:59
Shree9975 wrote:
Hi Bunuel
Engr2012
Can you please tell why did we took a=-3/4 and b=1
From what we got the values of a and b

Thanks

If you note carefully, that the formula written by Bunuel above for the shortest distance =

Line: $$ay+bx+c=0$$, point $$(x1,y1)$$

$$d=\frac{|ay1+bx1+c|}{\sqrt{a^2+b^2}}$$

So what it means is that the shortest distance of this line (ax+by+c=0) from (x1,y1) which is the origin (0,0) in our case is

$$d=\frac{|c|}{\sqrt{a^2+b^2}}$$. This is obtained by putting x1=0, y1=0,

For a and b, you need to bring the given equation of line :$$y = \frac{3}{4}*x-3$$ in the form $$ay+bx+c=0$$ to get : $$-4y+3x-12=0$$. Comparing these 2 equations we get,

a =-4, b =3 and c = -12

Substitute the above values of a,b,c,x1,y1 in the formula for d above to get:

$$d=\frac{|-12|}{\sqrt{(-3)^2+(4)^2}}=\frac{12}{5}=2.4$$ (Bunuel had divided this equation all across by 4. But you can also stick to this method).

And then the final required distance = 2.4 - radius of the circle = 2.4-1 = 1.4.

An alternate solution is below:

Refer to the attached figure for details of the variables used. You can see that the shortest distance to the line will be the perpendicular drawn from the center of the circle.

Also, in triangle POQ, right angled at O and OR is perpendicular to PQ.

In right triangle POQ , $$PQ^2=OP^2+OQ^2$$ ---> $$PQ^2 = 3^2+4^2$$ ---> $$PQ=5$$

Area of triangle POQ = $$0.5*OP*OQ = 0.5*OR * PQ$$ ---> $$OR = \frac{OP*OQ}{PQ}$$ ---> $$OR = \frac{3*4}{5}$$ ---> $$OR = 2.4$$

Finally,$$OR = OS + SR$$, OS = radius of the circle = 1 ---> $$SR = OR - OS = 2.4 -1 = 1.4$$. A is the answer.
Attachments

2015-07-27_16-21-12.jpg [ 21.98 KiB | Viewed 1382 times ]

_________________
CR Forum Moderator
Joined: 30 May 2019
Posts: 110
Location: United States
Concentration: Finance, General Management
Schools: CBS '22
GMAT 1: 610 Q46 V28
GPA: 3.37
WE: Analyst (Consulting)
Re: What is the least possible distance between a point on the circle x^2  [#permalink]

### Show Tags

02 Jul 2020, 01:45
absolutely the same question
https://gmatclub.com/forum/m13-183968.html
Bunuel, maybe merge?
Math Expert
Joined: 02 Sep 2009
Posts: 65854
Re: What is the least possible distance between a point on the circle x^2  [#permalink]

### Show Tags

02 Jul 2020, 01:57
mira93 wrote:
absolutely the same question
https://gmatclub.com/forum/m13-183968.html
Bunuel, maybe merge?

That question in GMAT Club's Tests (closed) forum So, all is good.
_________________
Re: What is the least possible distance between a point on the circle x^2   [#permalink] 02 Jul 2020, 01:57

Go to page   Previous    1   2   [ 23 posts ]

# What is the least possible distance between a point on the circle x^2

 new topic post reply Question banks Downloads My Bookmarks Reviews Important topics

 Powered by phpBB © phpBB Group | Emoji artwork provided by EmojiOne
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 1, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 0, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.5790297985076904, "perplexity": 3484.801638376933}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "absolute_threshold": 20, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2020-34/segments/1596439737206.16/warc/CC-MAIN-20200807172851-20200807202851-00199.warc.gz"}