Question

find the equation of the line which passes through p(1,-7) and meets the axes at A and B respectively so that 4AP-3BP=0.

Answer 1

Please see the attachment

Answer 2

28x -  3y = 49 is the equation of the line which passes through p(1,-7) and meets the axes at A and B respectively so that 4AP-3BP=0

Step-by-step explanation:

Let say line meet the x axis  at  A => ( A , 0)  point

& x axis  at  B => ( 0 , B)  point

4AP-3BP=0.

=> 4AP = 3BP

=> AP /BP = 3/4

=> AP : BP :: 3 : 4

point P (1 , -7) divides  A & B in 3 : 4 Ration

=>  1   = (3 * 0 + 4A)/(3 + 4)     &  -7  = (3B  + 4*0)/(3 + 4)

=> 1 = 4A/7      &  -7 = 3B/7

=> A = 7/4    &  B  =  -49/3

point A = ( 7/4 , 0)     B   = ( 0 , - 49/3)

Slope =  ( -49/3 - 0)/(0 - 7/4)  = 28/3

y = 28x/3 + c

=> -49/3 = 0 + c

=> c = -49/3

=> y = 28x/3 - 49/3

=> 3y = 28x - 49

=> 28x -  3y = 49

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