Find the equation of the line in general form parallel 5x + 6y - 10 = 0 at distance sqrt(61) from (-3, 7) with solution.

Answer 1

5x+6y-10=0

6y=-5x+10

y=-5x/6 +5/3

any parallel line will have the same slope =-5/6= coefficient of the x term

distance sqr61 from (-3,7)

it helps to plot the point

a perpendicular line through that point

will have a negative inverse slope = 6/5

y= 6x/5 +b

plug in the point (-3,7) to find b

7=-18/5 +b

b= 7+18/5=53/5

y=6x/5 +53/5

intersects

y=-5x/6 +b at a point sqr61 from (-3,7)

there are two lines, each sqr61 from (-3,7)

one intersects at (-8,1) it's the line y = -6x/5 - 17/3

the other intersects at (2,17), it's the line y =-6x/5 + 44/3

in general form they are

18x +15y +85 = 0

and

18x + 15y -220 = 0