What is the shortest distance from the line y = -2x+7 to the circle x^2 + y^2 = 6 ?
The answer is .681
If i had two points I could do this problem easily, but I keep running into problems.
forum.virtualchallengemeets.com
Your connection to the competitive math/science community. (Formerly texasmath.org)
07B-28 Shortest Distance Problem
5 posts
• Page 1 of 1
07B-28 Shortest Distance Problem
by moy2414 » Thu Feb 02, 2012 3:36 pm
- moy2414
- Typical User
- Posts: 5
- Joined: Mon May 10, 2010 11:08 pm
Re: 07B-28 Shortest Distance Problem
by 88bobcat » Mon Jul 09, 2012 3:43 pm
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
-
88bobcat - Celebrated Spammer
- Posts: 447
- Joined: Tue May 26, 2009 10:51 pm
- Location: Orange, TX
Re: 07B-28 Shortest Distance Problem
by 88bobcat » Mon Jul 09, 2012 3:48 pm
Rather than using differential calculus to determine the minimum distance, the point on the circle might also have been found by finding the intersection of the perpendicular, co-radial line and the circle.
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Substituting, [unparseable or potentially dangerous latex formula]
This yields [unparseable or potentially dangerous latex formula], and this yields the same result.
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Substituting, [unparseable or potentially dangerous latex formula]
This yields [unparseable or potentially dangerous latex formula], and this yields the same result.
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
-
88bobcat - Celebrated Spammer
- Posts: 447
- Joined: Tue May 26, 2009 10:51 pm
- Location: Orange, TX
Re: 07B-28 Shortest Distance Problem
by darksaber21 » Mon Jul 09, 2012 6:30 pm
Another method would be to use the following formula (shortest distance between a line and point, using the origin as a point), then subtract the radius of the circle to the answer, since the origin is the center of the circle, and the radius, should the distance be perpendicular to the line graph and, when extended, goes through the circle through the center (which it is and can):
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
Now I know the stakes, and I'm willing to show what I gots. I will see you all at state for the first and final time, so let's end the year with a bang! :)
MTHS - Class 5A, District VII, Region I
MTHS - Class 5A, District VII, Region I
- darksaber21
- Celebrated Spammer
- Posts: 477
- Joined: Tue May 29, 2012 6:20 pm
- Location: Arlington, TX
Re: 07B-28 Shortest Distance Problem
by 88bobcat » Mon Jul 09, 2012 7:02 pm
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
[unparseable or potentially dangerous latex formula]
-
88bobcat - Celebrated Spammer
- Posts: 447
- Joined: Tue May 26, 2009 10:51 pm
- Location: Orange, TX
5 posts
• Page 1 of 1
Return to Calculator Applications
Who is online
Users browsing this forum: No registered users and 9 guests