Math quiz (1 Viewer)

[Real Madrid]

It's a challenge to see who can answer these questions faster. The winner gets some UAI points

• Given two points A(3,-2) and B(-1,7), find the equation of the locus of P(x,y) if the gradient of PA is twice the gradient of PB.

• If R is the fixed point (3,2) and P is a movable point (x,y) find the equation of the locus of P if the distance PR is twice the distance from P to the line y=-1

 

[Timothy.Siu]

Given two points A(3,-2) and B(-1,7), find the equation of the locus of P(x,y) if the gradient of PA is twice the gradient of PB.

M of PA = y+2/x-3 M of AB = y-7/x+1

M of pa = 2M of BA
y+2/x-3=2(y-7)/x+1

(y+2)(x+1)=2(y-7)(x-3)
xy+y+2x+2=2(xy-3y-7x+21)
xy+y+2x+2=2xy-6y-14x+42
xy-7y-16x+40=0


If R is the fixed point (3,2) and P is a movable point (x,y) find the equation of the locus of P if the distance PR is twice the distance from P to the line y=-1

PR = root((x-3)^2+(y-2)^2)
P to line y=-1 = y+1 (edited due to mistake)

PR^2 =4P to line y=-1^2
x^2-6x+9+y^2-4y+4 = 4y+4
x^2-6x+9+y^2-8y=0

 

[tacogym27101990]

can you just admit you can't do the questions??
no ones gunna think less of you

 

[Real Madrid]

roflmao i cant do them

 

[Timothy.Siu]

P to line y=-1 = root((x-0)^2+(y+1)^2)

Did you use distance between P and (0, -1)? Are you supposed to use perpendicular distance?

yeah i guess i did it wrong
i changed it duno if its right now

 

[lyounamu]

It's a challenge to see who can answer these questions faster. The winner gets some UAI points

• Given two points A(3,-2) and B(-1,7), find the equation of the locus of P(x,y) if the gradient of PA is twice the gradient of PB.

• If R is the fixed point (3,2) and P is a movable point (x,y) find the equation of the locus of P if the distance PR is twice the distance from P to the line y=-1

i) y+2/x-3 = 2(y-7/x+1)
y+2/x-3 = 2y-14/x+1
(y+2)(x+1) = (2y-14)(x-3)
xy + 2x + y + 2 = 2xy - 14x - 6y + 42
xy - 16x - 7y + 40 = 0

ii) PD = AV(0 . x + 1 . y + 1)/1
= AV(y+1)
PR = SR((x-3)^2 + (y-2)^2))

PR = 2PD
SR((x-3)^2 + (y-2)^2)) = 2AV(y+1)
(x-3)^2 + (y-2)^2)) = 4(y+1)^2
x^2 - 6x + 9 + y^2 - 4y + 4 = 4y^2 + 8y + 4
x^2 - 6x + 9 -3y^2 -12y =0

EDIT: I forgot to demand my extra UAI points....I want them NOW.

 

[lyounamu]

Yay =]

Do you use something to type maths or do you type it like that?

Who are you referring to? Me or tim?

I guess it's tim.

 

[Timothy.Siu]

lol sorry about the mistake, forgot about that and i dont really know wat u mean,
i just do the answer in the reply and type it there

 

[Timothy.Siu]

Out of curiousity, do you work it out by typing it or do you work it out on paper first? Typing maths is annoying >.<"

i just type it, dont do it on paper wich is why all those mistakes

 

[lyounamu]

Oooh I was doing it on a paper I wrote one line of english on when I was trying to plan for an essay xD Scary how I'm procrastinating by doing maths :S

Typing straight on comp is the fastest way. But I cannot really gurantee the accuracy of the result though.

 

[jellybelly59]

im curious as to why real madrid has made so many threads for just locus questions .... can't you just keep it on one thread?

 

[Aplus]

Typing straight on comp is the fastest way. But I cannot really gurantee the accuracy of the result though.

Scanning would be the fastest way for me, I really do hate typing ^{and _etc.}