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.
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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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