SOLUTION: Find the equation of the line parallel to the line x-3y=2 and passing at a distance 2√10 from the given line.
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Question 828236: Find the equation of the line parallel to the line x-3y=2 and passing at a distance 2√10 from the given line.
Found 2 solutions by josgarithmetic, josmiceli:
Answer by josgarithmetic(39616) (Show Source): You can put this solution on YOUR website!
The given line is so any general point of the line is (x,(1/3)(x-2)).
You want another line, , to be distance from the given line. General point of the wanted line is (x,(1/3)x+b).
Distance Formula:
and what is needed is a formula for b in terms of x or no terms of x.
'
Two possible equations then would be and
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
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The slope of the line I want will
have a slope also
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I need a point that this line will go through
to get the equation
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Setting ,
So, the given line passes through (2,0)
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The line through this point and perpendicular
to the given line will have slope =
------------------------------------------------------
(1)
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Now I need to find the point on this line that is
distance from (2,0)
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Substituting from (1) above:
------------------
Plugging this into (1),
(1)
(1)
(1)
----------------------
Now I have
and the point ( 4,-6)
Using the point-slope formula:
answer
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Here's plots of the 3 lines:
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