# Locus problem + advice on completing the square (1 Viewer)

#### planino

##### Member

Find the equation of locus of point P(x,y) that moves so that the ratio PA to PB is 3:2 where A = (-6,5) B = (3, -1)

Also, how would you complete the square and put it into the form of a circle's equation for this question? (I have a feeling that this is not a 2U thing) :

5x2 + 132x + 6y2 + 99y + 56 = 770

#### superSAIyan2

##### Member
Thats not a bloody circle cos coeffs of x and y are different

PA^2 = (X+6)^2 + (Y-5)^2 = X^2 + 12X + Y^2 -10Y + 61
PB^2 = (X-3)^2 + (Y+1)^2 = X^2 - 6X + Y^2 + 2Y + 10

4PA^2 = 9B^2
Then i get 5x^2 -102x + 5y^2 +68y = 154 WHICH IS A CIRCLE SINCE COEFFS OF X AND Y ARE SAME

question should be in like maths for preskoolers

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#### planino

##### Member
mind completing the square for me and putting it in circle form?

#### superSAIyan2

##### Member
this question is stuffing you up ehhh

#### superSAIyan2

##### Member
stuff completing the square unless the question asks, if the question did ask just swear at your teacher - also if you complete the square how do you get a circle.

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#### SharkeyBoy

##### Member
4PA^2 = 9B^2
4(X^2 + 12X + Y^2 -10Y + 61) = 9(X^2 - 6X + Y^2 + 2Y + 10)
4X^2 +48X +4Y^2 -40Y +244 = 9X^2 -54X +9Y^2 +18Y + 90
5X^2 -102X +5Y^2 +58Y - 154 = 0

#### superSAIyan2

##### Member
lol i wrote 40 + 18 = 68 in ym working. your right sharkeyboy

+1'd.

haha thanks guys

#### planino

##### Member
Thank you all, but could someone please complete the square?

superSAIyan2, I hope you feel like an idiot now

#### planino

##### Member
Like I said, go back to playing with the bear, the chair and the people with games. Listen to the stories they have to tell, but don't skip to opening wide and coming inside. That's inshane ( )

Meh thanks for your help. It was a good tip, and I'll definitely take whatever you've said on board. After all, what's wrong with learning from the best? Thanks heaps

Sharkeyboy

#### SharkeyBoy

##### Member
haha yeh no worries, I'm not real sure how to simplify my answer any further though, if it's possible... (probably is)

#### superSAIyan2

##### Member
its ok planino - i received your message loud and clear. and i bet you are the one who got very excited from making your little pun. take it from the puns master - i make them deyly

#### planino

##### Member
Lol don't worry, I really don't care about that question now heh

#### superSAIyan2

##### Member
anyways out of curiosity have u looked at the skool 2u papers- theyre all full of differentiation stuff and thats not even examined this yr lol

#### superSAIyan2

##### Member
what question? my comment/post never referenced your question.

#### wannabesurgeon

##### Member
View attachment 2012-11-28 222840.pdf

Here is the locus one you asked for but in steps to see what is actually happening . Hope this helps! And I have never seen that circle one in 2U before?

now now children

play nice

#### Trebla

Please stay on topic. Discussions irrelevant to the topic at hand can be carried out via private messaging.

#### B3A13

##### Member
Please stay on topic. Discussions irrelevant to the topic at hand can be carried out via private messaging.
I look at completing the square like a quadratic,
e.g.

x^2 +2x+4 which can be factorised easily. You need to make the equation
5x2 + 132x + 6y2 + 99y + 56 = 770 into this to factorise. I just bring similar values together, by moving it around.

and then you HALVE the coefficent of x and y respectively and double them. Then you add this value to Each side of the equation.
The factorise and you should have the equation. For a circle,

I used (x-h)^2 + (y-k)^2 = r^2 which can be easily gained from rearranging the left side to squared form, right should be correct from above.

Worked for me,
hope it helps.

By the way I got this out of my books which I am selling at http://community.boredofstudies.org/showthread.php?t=295911 REALLY cheap, if you want have a look.

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