The distance between the parallel lines 8x+6y+5=0 and 4x+3y−25=0 is

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Question

The distance between the parallel lines

8 x + 6 y + 5 = 0

and

4 x + 3 y - 25 = 0

is

Options:

A . 73

B . 92

C . 112

D . 54

Answer: Option C
:
C
Distance between parallel lines

a x + b y + c_{1} = 0

and

a x + b y + c_{2} = 0

is

\frac{| c_{1} - c_{2} |}{\sqrt{a^{2} + b^{2}}}

Given lines are

8 x + 6 y + 5 = 0

and

4 x + 3 y - 25 = 0

or

8 x + 6 y - 50 = 0

∴

Required distance =

\frac{5 + 50}{\sqrt{8^{2} + 6^{2}}} = \frac{55}{10} = \frac{11}{2}

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