Help with locus qn. (1 Viewer)

[Getteral09]

Hey can anyone solve this maths problem? Point P moves so that PA^2 + PB^2 = 4 where A = (3,-1) and B = (-5, 4). Find the equation of the locus of P.
Thanks,Getteral

 

[Getteral09]

Yeh. there is a mistake. For some reason you can't get 25-6=47.

So how can you get the maths problem: (Point P moves so that PA^2 + PB^2 = 4 where A = (3,-1) and B = (-5, 4). Find the equation of the locus of P. ) to equal to the answer : 2x^2+4x+2y^2-6y+47?

 

[Ennaybur]

just from glancing at your work exphate, isnt it


PA^2 + PB^2 = 2^2 (rather than 16)

then you prolly follow the rest

 

[xlr8-crillz]

i got:
2x^2+4x+2y^2 -6y+43=0

 

[xlr8-crillz]

maybe u dont make 2 equations.

maybe it goes:

x^2+y^2-6x+2y+6 + x^2+10x + y^2 - 8y + +37=4

solve solve solve

and the answer is:
0= 2x^2+4x+2y^2-6y+ 47

 

[Getteral09]

maybe u dont make 2 equations.

maybe it goes:

x^2+y^2-6x+2y+6 + x^2+10x + y^2 - 8y + +37=4

solve solve solve

and the answer is:
0= 2x^2+4x+2y^2-6y+ 47

Nope, xlr8-crillz . That working out will eventually make the equation smaller i.e.
0= 2x^2+4x+2y^2-6y+ 39. And the other method happen to get the answer to
2x^2+4x+2y^2 -6y+43=0 which is wrong. Therefore i think there is a mistake in Maths In Focus's answer.

 

[xlr8-crillz]

sorry instead of:
x^2+y^2-6x+2y+6 + x^2+10x + y^2 - 8y + 37=4

it should have been:
x^2+y^2-6x+2y+10 + x^2+10x + y^2 - 8y + 41=4

i just typed it out wrong

and its like that above cause u werent meant to minus the 4 and make it all = 0 in your two smaller equations of PA and PB. but just to be sure, u probably u should get a pro to confirm the answer.

 

[followme]

PA²+PB²=2²
let the coordinate of P be (x,y)
use the distance formula:
PA=√(x-3)²+(y+1)²& PB=√(x+5)²+(y-4)²
PA²=(x-3)²+(y+1)²& PB²=(x+5)²+(y-4)²
ie (x-3)²+(y+1)²+(x+5)²+(y-4)²=4

solve...
The locus of P is 2X²+4X+2Y²-6Y+47=0

 

[xlr8-crillz]

ya........a lot more simpler. mine was just expanded i guess.

 

[jyu]

Hey can anyone solve this maths problem? Point P moves so that PA^2 + PB^2 = 4 where A = (3,-1) and B = (-5, 4). Find the equation of the locus of P.
Thanks,Getteral

No such point P can exist in the real x-y space
because AB = sqrt[(3+5)^2 + (-1-4)^2] = sqrt(89).
.: PA^2 + PB^2 > 4.

:wave: