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Simple coordinate geomety problem

by silent_hunter
Tags: coordinate, coordinate geomety, geomety, simple
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silent_hunter
#1
Feb18-14, 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
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 [itex]\frac{m-9-7m+17}{\sqrt{m^2 +1}}[/itex]=[itex]\pm[/itex]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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tiny-tim
#2
Feb18-14, 03:55 AM
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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 Quote by silent_hunter View Post
or,(6m-8)^2 =36(m^2 +1)
or, m=7/24
you should have put the intermediate step (6m-8) = 36(m2 +1)
silent_hunter
#3
Feb18-14, 04:28 AM
P: 13
Quote Quote by tiny-tim View Post

you should have put the intermediate step (6m-8) = 36(m2 +1)
thanks for your reply
(6m-8)2 =36(m2 +1)
in that step I squared both sides of the equation ,so the sign should go away.

tiny-tim
#4
Feb18-14, 05:34 AM
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Smile Simple coordinate geomety problem

sorry, i got that wrong

this is where you missed a solution
Quote Quote by silent_hunter View Post
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 = ∞ !
silent_hunter
#5
Feb18-14, 11:07 AM
P: 13
Quote Quote by tiny-tim View Post
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.
tiny-tim
#6
Feb18-14, 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 mx-y-7m-17=0
kdetro
#7
Feb19-14, 03:14 AM
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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