Simple coordinate geomety problem

by silent_hunter
Tags: coordinate, coordinate geomety, geomety, simple
 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 y-17=m(x-7) or, mx-y-7m-17=0 now the line have a distance of 6 units from point(1,9). so $\frac{m-9-7m+17}{\sqrt{m^2 +1}}$=$\pm$6 or,(6m-8)2 =36(m2 +1) or, m=7/24 so the equation of line becomes 7x-24y+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 x-7=0 which is parallel to the y-axis.(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?
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P: 26,148
hi silent_hunter!

(try using the X2 button just above the Reply box )

you lost half the solutions when you took the square-root of this line …
 Quote by silent_hunter or,(6m-8)^2 =36(m^2 +1) or, m=7/24
you should have put the intermediate step (6m-8) = ±36(m2 +1)
P: 13
 Quote by tiny-tim you should have put the intermediate step (6m-8) = ±36(m2 +1)
(6m-8)2 =36(m2 +1)
in that step I squared both sides of the equation ,so the ± sign should go away.

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P: 26,148
Simple coordinate geomety problem

sorry, i got that wrong

this is where you missed a solution …
 Quote by silent_hunter the equation of line passing through(7,17) and having slope m is y-17=m(x-7) or, mx-y-7m=17=0
… you missed out m = ∞ !
P: 13
 Quote by tiny-tim sorry, i got that wrong this is where you missed a solution … … you missed out m = ∞ !
sorry I made a typing mistake.
Its mx-y-7m-17=0 but I didn't get what you said. Would you please elaborate?Thanks.
 Sci Advisor HW Helper Thanks P: 26,148 one of the two lines is x = 7, isn't it? (with slope ∞) that doesn't come up for any m in mx-y-7m-17=0
 P: 1 if you think of it as (y-9)^2 + (x-1)^2 = 36 then: y=cos(3(x-1))+15.91 or so should hit twice. I'll bet some kind of absolute value function would hit three times.

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