Question

Find the distance between the parellel lines 5x-3y-4=0 and10x-6y-9=0

Answer 1

Answer:

• Distance between two parallel lines are 1/2√34

Step-by-step explanation:

Given:

• Lines : 5x - 3y - 4 = 0 and 10x - 6y - 9 = 0

To Find:

• Distance between them.

Now,

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

=> 10x - 6y - 9 = 0 .......(2)

Now, we will multiply equation (1) by 2, to make them equal.

=> 10x - 6y - 8 = 0 .......(3)

Now, we know that

=> Distance between parallel lines = (lC₁ - C₂l)/√a² + b²

Now, put the values in the equation.

=> (l-8 + 9l)/√10² + (-6)²

=> 1/√100 + 36

=> 1/√136

=> 1/√2 × 2 × 2 × 17

=> 1/2√34.

Hence, distance between two parallel lines are 1/2√34.

Answer 2

$\tt{\huge{\pink{Hello !!! }}}$

$\tt{\blue{Formulae \: Used \::- }}$

$\begin{lgathered}ax+by+c_1=0\\ \:and\: ax+by+c_2=0\: is\\\\d =\frac{|c_1-c_2|}{\sqrt{a^2+b^2}}\end{lgathered}$

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5x -3y - 4 = 0

10x - 6y - 9 = 0

Divide by 2

5x -3y -( 9/2) = 0

Distance :

$\begin{lgathered}d =\frac{|-4-(\frac{-9}{2})|}{\sqrt{5^2+(-3)^2}}\\\\d =\frac{|-4+(\frac{9}{2})|}{\sqrt{25+9}}\\\\d =\frac{|(\frac{1}{2})|}{\sqrt{34}}\\\\d =\frac{1}{2\sqrt{34}}\end{lgathered}$

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