Time remaining:
Mathematics Locus of a point

label Mathematics
account_circle Unassigned
schedule 0 Hours
account_balance_wallet $5

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

Oct 23rd, 2017

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

Studypool's Notebank makes it easy to buy and sell old notes, study guides, reviews, etc.
Click to visit
The Notebank
...
Oct 23rd, 2017
...
Oct 23rd, 2017
Oct 24th, 2017
check_circle
Mark as Final Answer
check_circle
Unmark as Final Answer
check_circle
Final Answer

Secure Information

Content will be erased after question is completed.

check_circle
Final Answer