Question 1186111
<br>
(1) It should be clear that there will be two such lines -- one on each side of the given point.<br>
(2) Something is missing in the equation of the given line... but it doesn't matter.<br>
Every line parallel to the given line has an equation of the form<br>
5x+6y+c=0<br>
The distance from the point (-3,7) to the line with equation 5x+6y+c=0 is<br>
{{{abs((5(-3)+6(7)+c)/sqrt(5^2+6^2))}}}<br>
The distance from (-3,7) to the line is {{{sqrt(61)}}}<br>
{{{abs((5(-3)+6(7)+c)/sqrt(61))=sqrt(61)}}}
{{{abs(-15+42+c)=61}}}<br>
(1) -15+42+c=61 --> c=34
(2) -15+42+c=-61 --> c=-88<br>
ANSWERS:
(1) 5x+6y+34=0
(2) 5x+6y-88=0<br>
A graph, showing the two lines (red and green) a distance of sqrt(61) from (-3,7):<br>
{{{drawing(500,500,-20,10,-10,20,graph(500,500,-20,10,-10,20,(-5/6)x-34/6,(-5/6)x+88/6,(6/5)x+53/5),circle(-3,7,0.2),locate(-7,8,"(-3,7)"),circle(-8,1,0.2),locate(-7,2,"(-8,1)"),circle(2,13,0.2),locate(3,14,"(2,13)"))}}}<br>