The line L given by \frac{x}{5}+\frac{y}{b}=1  passes through the point (13, 32). The line K is parallel to L and has the equation \frac{x}{c}+\frac{y}{3}=1. Then the distance between L and K is

  • Option 1)

    \frac{23}{\sqrt{15}}\;

  • Option 2)

    \; \; \sqrt{17}\;

  • Option 3)

    \; \frac{17}{\sqrt{15}}\;

  • Option 4)

    \; \frac{23}{\sqrt{17}}

 

Answers (1)
A Aadil Khan

As we learnt in 

Condition for parallel lines -

m_{1}= m_{2}

- wherein

Here m_{1},m_{2} are the slope of two lines

 

 and

Distance between two parallel lines -

\rho =\frac{\left | c_{2}-c_{1} \right |}{\sqrt{a^{2}+b^{2}}}

 

- wherein

\rho is the distance between ax+by+c_{1}=0  and ax+by+c_{2}=0

 

 \frac{x}{5}+ \frac{y}{b}= 1

Put (13, 32)

\frac{13}{5}+\frac{y}{b}= 1

\Rightarrow b= -20

\frac{x}{5}- \frac{y}{20}= 1

y = 4x-20

So, m = 4

Also, \frac{x}{c}+ \frac{y}{3} = 1\:,\:m = \frac{-3}{c}

\frac{-3}{c}= 4\; \Rightarrow c=\frac{-3}{4}

Equation is -4x + y = 3

Distance \frac{\left | 3+20 \right |}{\sqrt{17}}=\frac{23}{\sqrt{17}}


Option 1)

\frac{23}{\sqrt{15}}\;

This option is incorrect.

Option 2)

\; \; \sqrt{17}\;

This option is incorrect.

Option 3)

\; \frac{17}{\sqrt{15}}\;

This option is incorrect.

Option 4)

\; \frac{23}{\sqrt{17}}

This option is correct.

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