Simple coordinate geomety problem


by silent_hunter
Tags: coordinate, coordinate geomety, geomety, simple
silent_hunter
silent_hunter is offline
#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?
Phys.Org News Partner Mathematics news on Phys.org
Hyperbolic homogeneous polynomials, oh my!
Researchers help Boston Marathon organizers plan for 2014 race
'Math detective' analyzes odds for suspicious lottery wins
tiny-tim
tiny-tim is offline
#2
Feb18-14, 03:55 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
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
silent_hunter is offline
#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
tiny-tim is offline
#4
Feb18-14, 05:34 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
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
silent_hunter is offline
#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
tiny-tim is offline
#6
Feb18-14, 11:33 AM
Sci Advisor
HW Helper
Thanks
tiny-tim's Avatar
P: 26,167
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
kdetro is offline
#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.


Register to reply

Related Discussions
simple coordinate transformation question General Math 1
A simple question about coordinate sytems General Physics 5
Coordinate systems - finding optimal? simple conceptual question Calculus 2
VERY SIMPLE Coordinate Geometry Precalculus Mathematics Homework 30
"Simple" Coordinate Problem Introductory Physics Homework 6