Question

Find the distance between the parallel straight lines
5x-3y-4=0,10x-6y-9=0

Answer 1

10x – 6y – 8 = 0, 10x – 6y – 9 = 0

Answer 2

Question :-

• Find the distance between the parallel straight lines 5x - 3y - 4 = 0, 10x - 6y - 9 = 0.

Answer

Given :-

• Two parallel lines 5x - 3y - 4 = 0 and 10x - 6y - 9 = 0

To find :-

• Distance between parallel lines.

Formula used :

• Let us consider two parallel lines ax + by + c = 0 and ax + by + d = 0, then distance between these two parallel lines is given by

$\bf \:Distance = \dfrac{ |c - d| }{ \sqrt{ {a}^{2} + {b}^{2} } }$

Solution :-

Consider the line

5x - 3y - 4 = 0.........(1)

Multiply (1) by 2, we get

10x - 6y - 8 = 0.

Now, we have to find the distance between 10x - 6y - 8 = 0 and 10x - 6y - 9 = 0, using the formula

$\bf \:Distance = \dfrac{ |c - d| }{ \sqrt{ {a}^{2} + {b}^{2} } }$

On substituting the values, c = - 8, d = - 9, a = 10, b = - 6, we get

$\bf \:Distance = \dfrac{ | - 8 - ( - (9)| }{ \sqrt{ {10}^{2} + {( - 6)}^{2} } }$

$\bf\implies \:Distance = \dfrac{1}{ \sqrt{100 + 36} }$

$\bf\implies \:Distance = \dfrac{1}{ \sqrt{136} }$

$\bf\implies \:Distance = \dfrac{1}{ \sqrt{2 \times 2 \times 2 \times 17} }$

$\bf\implies \:Distance = \dfrac{1}{2 \sqrt{34} } \: units$