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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

Dec 19th, 2014

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 = 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

y

Dec 19th, 2014

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