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ICSE Class 10 Answered

Find the equation of line which passes through the point (3,4) and the sum of its intercepts on the axes is 14.
Asked by Vaibhav | 04 Dec, 2017, 09:40: PM
answered-by-expert Expert Answer
begin mathsize 16px style Let space the space equation space of space line space be space straight x over straight a plus straight y over straight b equals 1 This space passes space through space left parenthesis 3 comma space 4 right parenthesis. rightwards double arrow 3 over straight a plus 4 over straight b equals 1 Now comma space straight a plus straight b equals 14 rightwards double arrow straight b equals 14 minus straight a Then comma space we space have 3 over straight a plus fraction numerator 4 over denominator 14 minus straight a end fraction equals 1 rightwards double arrow fraction numerator 42 minus 3 straight a plus 4 straight a over denominator 14 straight a minus straight a squared end fraction equals 1 rightwards double arrow 42 plus straight a equals 14 straight a minus straight a squared rightwards double arrow straight a squared minus 13 straight a plus 42 equals 0 rightwards double arrow straight a squared minus 7 straight a minus 6 straight a plus 42 equals 0 rightwards double arrow straight a left parenthesis straight a minus 7 right parenthesis minus 6 left parenthesis straight a minus 7 right parenthesis equals 0 rightwards double arrow left parenthesis straight a minus 7 right parenthesis left parenthesis straight a minus 6 right parenthesis equals 0 rightwards double arrow straight a equals 7 space or space 6 when space straight a equals 7 comma space straight b equals 14 minus 7 equals 7 when space straight a equals 6 comma space straight b equals 14 minus 6 equals 8 Thus comma space we space have straight x over 7 plus straight y over 7 equals 1 space space and space space straight x over 6 plus straight y over 8 equals 1 rightwards double arrow straight x plus straight y equals 7 space space and space space space 4 straight x plus 3 straight y equals 24 end style
Answered by Rashmi Khot | 05 Dec, 2017, 10:03: AM

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