SOLUTION: Find the equation of the line parallel to 5x + 6y 10 = 0 at a 1 distance √61 from (-3, 7).

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Question 1186111: Find the equation of the line parallel to 5x + 6y 10 = 0 at a 1 distance √61 from (-3, 7).
Answer by greenestamps(13200) About Me  (Show Source):
You can put this solution on YOUR website!


(1) It should be clear that there will be two such lines -- one on each side of the given point.

(2) Something is missing in the equation of the given line... but it doesn't matter.

Every line parallel to the given line has an equation of the form

5x+6y+c=0

The distance from the point (-3,7) to the line with equation 5x+6y+c=0 is

abs%28%285%28-3%29%2B6%287%29%2Bc%29%2Fsqrt%285%5E2%2B6%5E2%29%29

The distance from (-3,7) to the line is sqrt%2861%29

abs%28%285%28-3%29%2B6%287%29%2Bc%29%2Fsqrt%2861%29%29=sqrt%2861%29
abs%28-15%2B42%2Bc%29=61

(1) -15+42+c=61 --> c=34
(2) -15+42+c=-61 --> c=-88

ANSWERS:
(1) 5x+6y+34=0
(2) 5x+6y-88=0

A graph, showing the two lines (red and green) a distance of sqrt(61) from (-3,7):