Question

Distance between the lines 15x+9y+14=0 and 10x+6y−14=0 is​

Answer 1

Answer:

3(5x+y)+14=0

5x+y=-14/3

2(5x-3y)-14=0

5x-3y=14/2

5x-3y=7

Answer 2

Answer:

35/3√34

Step-by-step explanation:

Line 1 = 15x+9y+14=0 ..(1)

Divide equation(1) by 3, we get

5x+3y+14/3=0

Line 2 = 10x+6y-14=0 ...(2)

Divide equation(2) by 2, we get

5x+3y-7=0

Slope of Line 1 (m1) is =-a/b

                                    =-5/3

Slope of Line 2 (m2) is =-a/b

                                      =-5/3

m1=m2

Therefore, Line 1 & Line 2 are parallel

Distance between two parallel lines

d = |c1-c2| / √a^2+b^2

 =14/7-(-7)/√(5)^2+(3)^2

 =14/7+7/√34

 =35/3√34