| Author | Calculus/Geometry question challenge |
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here's a pretty cool and tough problem, whoever answers it correctly first will receive a prize from me =)
You are given two circles, the equation of the first circle is:
(x^2)+(y^2)=1 (so the mid-point of the circle is located at (0,0) and its radius is 1)
the equation of the 2nd circle is:
[(x-4)^2]+(y^2)=4 (so the mid-point is located at (4,0) and its radius is 2)
Objectives:
draw the (two) external tangents of these circles, and (two) internal tangents and:
>>Find the slopes of all 4 tangent lines<<
good luck, and again.. the winner will receive a prize =) |
equation of the first circle is:
(x^2)+(y^2)=1
to be more accurate, the equation is (x^2)+(y^2)=1^2 but the 1^2 is 1 anyway. |
| The external tangents' slopes are 1/4 and -1/4 |
| have to show the work, it's easy to do with a online program ;P |
| Am i doin your homework for you :p |
| hahah no, this is a question that took me a couple of hours to figure out, i want to see who else can get it =) |
| oh haha well i suck at geometry but my friend is working on it |
i dont know what do you mean with "external tangent" and "internal tangent". dont learn math using english. i try to draw it first. is this you mean ?
https://www.lordswm.com/photo_pl_photos.php?aid=10073 |
for cakur:
your image is a bit off, the tangents are perpendicular to the radius of both circles, but you got the idea |
Here is your geometry homework:
https://www.lordswm.com/photo_pl_photos.php?aid=10077 |
| When i get into a University {if i can} I am going to have to study Geometry for atleast a year before i understand it.. -_-" |
for Seiran_1045:
lol it's not that hard... cakur got it, but he didnt finish it.
for naviron:
i dont even know what you did.. i did it the way cakur did it you did some crazy stuff..
and as i said before, this isnt my homework |
the first image is draw 2 external tangent and 2 internal tangent.
second image is to calculate the degree of external tangent. look at bold triangle, we have alpha with cosinus = 1/4. which mean slope = 1/sqrt(3) = 0.577. +0.577 and -0.577.
third image is to calculate the degree of internal tangent. look at bold triangle, we have alpha with sinus = 3/4. which mean slope = 3/sqrt(7) = 1.133. +1.133 and -1.133. |
| Prize to cakur, he got it =) |
| closed by Lord Gangstarr (2012-01-13 08:26:14) |
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