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Home / Doubts and Solutions/JEE/Mathematics

A STRAIGTH LINE PASSING THROUGH THE POINT A(2,3) HAS INCLINATION 45 degree AND INTERSECT THE LINE 2x-3y+9=0 AT POINT P.FIND THE DISTANCE AP.

Asked by neeraj.unnao 14th November 2016, 4:43 PM
Answered by Expert
Answer:
tan open parentheses 45 degree close parentheses space equals space 1 E q u a t i o n space o f space t h e space l i n e space p a s sin g space t h r o u g h space A left parenthesis 2 comma space 3 right parenthesis space a n d space h a s space i n c l i n a t i o n space 45 degree space i s space g i v e n space b y left parenthesis y minus 3 right parenthesis space equals space 1 left parenthesis x minus 2 right parenthesis y space equals space x plus 1............. left parenthesis i right parenthesis L i n e space g i v e n space b y space e q space left parenthesis i right parenthesis space i n t e r s e c t space 2 x minus 3 y plus 9 equals 0 space P o i n t space o f space i n t e r s e c t i o n space o f space y space equals space x plus 1 space space a n d space space y space equals fraction numerator 2 x plus 9 over denominator 3 end fraction space i s space g i v e n space b y space x plus 1 space equals space fraction numerator 2 x plus 9 over denominator 3 end fraction 3 x plus 3 equals 2 x plus 9 x space equals space 6 P u t space x space equals space 6 space i n space e q space left parenthesis i right parenthesis space w e space g e t comma y space equals space x space plus space 1 space equals space 6 space plus space 1 space equals space 7 P o i n t space o f space i n t e r s e c t i o n space i s space P left parenthesis 6 comma space 7 right parenthesis. u sin g space d i s tan c e space f o r m u l a comma A P space equals square root of open parentheses 6 minus 2 close parentheses squared plus open parentheses 7 minus 3 close parentheses squared end root equals square root of 16 plus 16 end root equals 4 square root of 2 space u n i t s space
Answered by Expert 15th November 2016, 10:43 AM
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