Find the distance between lines 8x−15y+5=0 and 16x−30y−12=0.

Step-by-step explanation:

Lines and are parallel because

The distance between two lines and can be calculated using formula

Divide the equation of the second line by 2:

Hence, the distance between two lines is

d = .

Step-by-step explanation:

We, have given two line lines 8x-15y+5=0 and 16x−30y−12=0. These two lines are parallel because it follows parallel condition: .

We need to find the distance between these two parallel lines.

We know that distance formula, between two parallel line:

d =

We have these two equation 8x−15y+5=0 and 16x−30y−12=0 but its coffiecients are not same, then we will first same coffiecients:

8x−15y+5=0, we can written as 8x-15y = -5

16x−30y−12=0, we can written as 16x-30y = 12, common 2 from these equation: 8x-15y = 12/2 = 6. Now, both lines have same cofficients.

Applying distance formula,

d =

d =

d =

d =

Therefore, distance between the these two lines are 11/17.