Simple coordinate geomety problemby silent_hunter Tags: coordinate, coordinate geomety, geomety, simple 

#1
Feb1814, 12:14 AM

P: 13

I'm not sure where to post this. So I'm posting in the General Math section.This is a simple coordinate geometry problem: We have to find the equation of line(s) passing through the point (7,17) and having a distance of 6 units from the point(1,9).
Now I'm posting my approach: the equation of line passing through(7,17) and having slope m is y17=m(x7) or, mxy7m17=0 now the line have a distance of 6 units from point(1,9). so [itex]\frac{m97m+17}{\sqrt{m^2 +1}}[/itex]=[itex]\pm[/itex]6 or,(6m8)^{2} =36(m^{2} +1) or, m=7/24 so the equation of line becomes 7x24y+359 =0 This way we get only line.But if you draw it in a graph paper,you'll see that there should be another line which is x7=0 which is parallel to the yaxis.(draw a circle of radius 6 from (1,9) and then draw tangent from (7,17) to the circle). I think we can't get the second one because it has undefined slope. My question is how can I get the second line without plotting in graph? 



#2
Feb1814, 03:55 AM

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hi silent_hunter!
(try using the X^{2} button just above the Reply box ) you lost half the solutions when you took the squareroot of this line … 



#3
Feb1814, 04:28 AM

P: 13

(6m8)^{2} =36(m^{2} +1) in that step I squared both sides of the equation ,so the ± sign should go away. 



#4
Feb1814, 05:34 AM

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Simple coordinate geomety problem
sorry, i got that wrong
this is where you missed a solution … … you missed out m = ∞ ! 



#5
Feb1814, 11:07 AM

P: 13

Its mxy7m17=0 but I didn't get what you said. Would you please elaborate?Thanks. 



#6
Feb1814, 11:33 AM

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one of the two lines is x = 7, isn't it?
(with slope ∞) that doesn't come up for any m in mxy7m17=0 



#7
Feb1914, 03:14 AM

P: 1

if you think of it as (y9)^2 + (x1)^2 = 36
then: y=cos(3(x1))+15.91 or so should hit twice. I'll bet some kind of absolute value function would hit three times. 


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