Determine the distance

A

Ana.stasia

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Determine the equations of lines containing point A (2,5) and whose distance from point N (5,1) is equal to 3.

I honestly have no idea how to connect the two formulas i have in squares.

IMG_20210211_141708.jpg
 
the distance between points A and N is 5 ... why do you have d = 3 written down?

the slope between points A and N is [MATH]m=-\dfrac{4}{3}[/MATH]
the equation of the line passing through point A has slope perpendicular to segment AN

[MATH]y - 5 = m_{\perp}(x-2)[/MATH]
now, how does one determine a perpendicular slope?
 
skeeter said:
the distance between points A and N is 5 ... why do you have d = 3 written down?

the slope between points A and N is [MATH]m=-\dfrac{4}{3}[/MATH]
the equation of the line passing through point A has slope perpendicular to segment AN

[MATH]y - 5 = m_{\perp}(x-2)[/MATH]
now, how does one determine a perpendicular slope?
Click to expand...

Read the problem.
 
Ana.stasia said:
Determine the equations of lines containing point A (2,5) and whose distance from point N (5,1) is equal to 3.

I honestly have no idea how to connect the two formulas i have in squares.

View attachment 25077
Click to expand...
To continue the method you are using, you can solve the first equation for C and substitute that in the second equation. Then you can try to solve for A/B (because only the ratio can be determined - or you could take B=1 and solve for A).

I don't get a nice result, but I may have been rushing.

I think there may be more efficient ways to solve the problem; vectors might be of use, or just geometry (there are some very nice right triangles hidden in the problem).
 
note the horizontal distance between A and N is 3 [MATH]\implies x = 2[/MATH] is one line that passes through A and is a distance of 3 from N.
 
Beer soaked request follows.
Ana.stasia said:
Determine the equations of lines containing point A (2,5) and whose distance from point N (5,1) is equal to 3.

I honestly have no idea how to connect the two formulas i have in squares.

View attachment 25077
Click to expand...
It would probably help a lot if you could also post a screenshot of the problem from your book (in addition of course to the screenshot of your attempts). By the way, who is the author of your book?
 
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