- #1

silent_hunter

- 13

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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)

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?

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(m^{2}+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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