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 | 4th Dec, 2017, 09:40: PM

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 | 5th Dec, 2017, 10:03: AM