समांतर रेखाओं ` 15x + 8 y - 34 = 0 ` तथा ` 15x + 8y +31 = 0 ` के बीच की दुरी ज्ञात कीजिये |

Explanation

हम लिख सकते है -
` 15 x + 8y - 34 = 0 rArr y = - ( 15 ) / ( 8 ) x + ( 17 ) / ( 4 ) " " `...(i)
तथा ` 15 x + 8 y + 31 = 0 rArr y = - ( 15 ) /( 8 ) x - ( 31 ) /( 8) " " `...(ii)
स्पष्टतः ` m _ 1 = m _ 2 = m = ( - 15 )/ ( 8 ) `
` c _ 1 = ( 17 ) /( 4 ) , c _ 2 = - (31 ) /( 8 ) `
रेखाओं के बीच की अभीष्ट दुरी ` = ( |c _ 2 - c _ 1 | ) / ( sqrt ( 1 + m ^ 2 )) `
` = (| - ( 31 ) /( 8 ) - ( 17 ) /( 4 ) | ) /( sqrt ( 1 + ( - ( 15 ) /( 8) ) ^ 2 ) = ( | ( - 65 ) / ( 8)| ) /( sqrt ( ( 289)/ ( 64 )) ) = ( 65 ) /( 8 ) xx ( 8 ) /( 7 ) xx ( 8 ) /( 17 ) = ( 65 ) /( 17 ) ` मात्रक