Mathematics Locus of a point
Mathematics

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Great 1 half correct answer... to a high school maths question.
Find the equation of the locus of a point P that moves such the distance from P to the lines 3x  4y + 1 = 0 and 12x + 5y +3 = 0 is in the ratio 3:1
3x  4y + 1 = 0
12x + 5y + 3 = 0
Simplify, Find x from the first equation and substitute x with the final result in a second equation to find y within the next steps:
1)
3x = 4y  1, x = (4 y 1) / 3
5y =  3  12x, y =  (3 + 12x) / 5
2)
x = (4 ((3+12x)/5 )  1) / 3
x = ((( 12  48x) / 5)  1) /3
x = (( 12  48x  5) / 5) /3
x = (( 17  48x)/5 ) /3
x = 17/15  48x/15 = (17  48x)/15
x  ((17+48x)/15) = 0
x/15  (17+48x)/15 = 0
(15x + 48x + 17)/15 = 0
(63x + 17)/15 =0
63x = 17
x =  17/63
3)
y = ( (3 + 12( 17/63))) /5
y =  (( 3 – 204/63) )/5
y =  ((189  204)/63)/5
y = (15/63)/5
y = 1/21
Hope it helps!
3x  4y + 1 = 012x + 5y + 3 = 0
Simplify, Find x from the first equation and substitute x with the final result in a second equation to find y within the next steps:
1)
3x = 4y  1, x = (4 y 1) / 3
5y =  3  12x, y =  (3 + 12x) / 5
2) x = (4 ((3+12x)/5 )  1) / 3
x = ((( 12  48x) / 5)  1) /3
x = (( 12  48x  5) / 5) /3
x = (( 17  48x)/5 ) /3
x = 17/15  48x/15 = (17  48x)/15
x  ((17+48x)/15) = 0
x/15  (17+48x)/15 = 0
(15x + 48x + 17)/15 = 0
(63x + 17)/15 =0
63x = 17
x =  17/63
y
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