Question

Distance between the lines 5x-12y+2=0 and 5x-12y-3=0 is

Answer 1

Hey Mate here is ur answer
The difference between the two lines is just of an integer with the power of -5
Hope it helps...

Answer 2

Answer:

The constant term in the both equation are 2 and -3 which are opposite sign. Hence origin lies between them.

Now using formula to find distance between two line,

$\: \: \sf \bf \: d = \frac{ |c_1| \: + |c_2| }{ \sqrt{ {a}^{2} + {b}^{2} } } \\ \\ \implies \sf \frac{ |2| + | - 3| }{ \sqrt{ {(5)}^{2} + {( - 12)}^{2} } } \\ \\ \implies \: \frac{5}{ \sqrt{25 + 144} } \\ \\ \implies \: \frac{5}{ \sqrt{169} } \\ \\ = \tt \pink {\frac{5}{13} ans}$

Note:-

The distance between the line is,

$\: \: \: \: \: \: \: \sf \: d \: = \frac{ \lambda}{ \sqrt{( {a}^{2} + {b}^{2}) }}$

(i.) λ = |c₁ - c₂|, if both the lines are on the same side of the origin.

(ii.) λ = |c₁| + |c₂|, is both the lines are on the opposite side of the origin.