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Home / Doubts and Solutions/KERALA/Class 11 Science/Mathematics

Find the distence between 4x-3y-9=0 and 8x-6y-21=0

Asked by Deebu 28th December 2014, 12:29 AM
Answered by Expert
Answer:
G i v e n space l i n e s space a r e space p a r a l l e l space t o space e a c h space o t h e r. C o n s i d e r space t h e space e q u a t i o n space 4 x minus 3 y minus 9 equals 0 T h e space l i n e space 4 x minus 3 y minus 9 equals 0 space c u t s space t h e space y minus a x i s space a t space left parenthesis 0 comma space minus 3 right parenthesis T h e r e f o r e comma space t h e space d i s tan c e space b e t w e e n space t h e space l i n e s 4 x minus 3 y minus 9 equals 0 space space a n d space 8 x minus 6 y minus 21 equals 0 space i s space t h e space p e r p e n d i c u l a r space d i s tan c e space f r o m space t h e p o i n t space left parenthesis 0 comma minus 3 right parenthesis space t o space t h e space l i n e space 8 x minus 6 y minus 21 equals 0. T h e r e f o r e comma d equals open vertical bar fraction numerator A x subscript 1 plus B y subscript 1 plus C over denominator square root of A squared plus B squared end root end fraction close vertical bar subscript open parentheses 0 comma minus 3 close parentheses end subscript rightwards double arrow d equals open vertical bar fraction numerator 8 x subscript 1 minus 6 y subscript 1 minus 21 over denominator square root of 8 squared plus open parentheses minus 6 close parentheses squared end root end fraction close vertical bar subscript open parentheses 0 comma minus 3 close parentheses end subscript rightwards double arrow d equals open vertical bar fraction numerator 8 cross times 0 minus 6 cross times open parentheses minus 3 close parentheses minus 21 over denominator square root of 8 squared plus open parentheses minus 6 close parentheses squared end root end fraction close vertical bar rightwards double arrow d equals open vertical bar fraction numerator 18 minus 21 over denominator square root of 64 plus 36 end root end fraction close vertical bar rightwards double arrow d equals open vertical bar fraction numerator minus 3 over denominator square root of 100 end fraction close vertical bar rightwards double arrow d equals 3 over 10 space u n i t s
Answered by Expert 28th December 2014, 1:43 PM
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