A locus problem. (1 Viewer)

[darkcounty]

A and B are the fixed points (a,o) and (-a,o). Find the locus of P(x,y) such that the gradient of AP is twice the gradient of BP.

The answer is 3a=x.

Can someone show me the working to this problem?

 

[addikaye03]

A and B are the fixed points (a,o) and (-a,o). Find the locus of P(x,y) such that the gradient of AP is twice the gradient of BP.

The answer is 3a=x.

Can someone show me the working to this problem?

m(AP)=2m(BP) [The m just stands for gradient]

Using m=(y2-y1)/(x2-x1)

m(AP)=y/(x-a)

m(GP)=y/x+a

y/(x-a)=2y/(x+a) [Since m(AP)=2m(BP)]

y(x+a)=2y(x-a)

yx+ya=2yx-2ya

yx=3ya

x=3a, As required

 

[darkcounty]

Ah, that's brilliant thanks, repped.