"Harder 2U" Ext 1 Maths Help (1 Viewer)

[EmeraldTempest]

G'Day guys.
I'm wondering if anyone can help me? I have a question from a ext 1 maths yearly past paper in the Yr 11 Locus and Parabola topic. I'm not sure how to approach it!

Find the equation of the locus that moves so that it is always twice the distance from P(x,y) to A(3,7) as it is from P to B(-2,-5). Thus prove that the locus is a circle, find its radius and centre.

I have gone through the processes of 2 x Distance PA = Distance PB... but i'm getting an answer of a circle centre (8,19) with a radius of 32.9 - which seems WAY to big!

Please give it a go for me.
Thanks

EmeraldTempest

 

[spammy679]

hmm i got the same centre but radius of 18.39

 

[duckcowhybrid]

2PA=PB
4PA^2=PB^2

No more messy surds. I'll work out the answer later.

 

[spammy679]

2PA=PB
4PA^2=PB^2

No more messy surds. I'll work out the answer later.

damn i always forget to square the 2

 

[spammy679]

its actually PA=2PB

it has centre ( -11/3 , -9) and radius 26/3 units

 

[Divided_By_Zero]

wow well i got radius of 28.1 where did i go wrong

 

[xXmuffin0manXx]

lol i got centre (14/3,11) and radius 26/3 which is about 8.7

 

[Divided_By_Zero]

Oh wait i see what i did.

 

[duckcowhybrid]

its actually PA=2PB

it has centre ( -11/3 , -9) and radius 26/3 units

Yeah your first part is correct. Question is worded awkwardly.

 

[EmeraldTempest]

Thanks everyone,

that helped clear it up. I obviously need to pay closer attention to the exact wording of questions.

Thankyou once again,

EmeraldTempest