locus (1 Viewer)

simDS · Aug 23, 2009

<DIR>hi... hey can anyone solve this

... thanks....

The point P(x,y) moves so that its distsnce PA from the point A(1,5) is always twice its distance PB from the point B(4,-1). show tjat the equation of the locus is
x^2 + y^2 - 10x + 6y + 14 =0
</DIR>

ninetypercent · Aug 23, 2009

PA = 2PB

$\sqrt{(x-1)^2 + (y-5)^2} = 2\sqrt{(x-4)^2 + (y+1)^2}$
$\sqrt{x^2 - 2x+1+y^2 - 10y + 25 } = 2\sqrt{x^2 -8x + 16 + y^2 + 2y + 1}$
$x^2 - 2x + 1 + y^2 - 10y + 25 = 4(x^2 - 8x + 16 + y^2 + 2y + 1)$
$x^2 - 2x + 1 + y^2 - 10y + 25 = 4x^2 - 32x + 64 + 4y^2 + 8y + 4$
$-3x^2 + 30x - 42 - 3y^2 - 18y = 0$
divide by - 3
rearrange
$x^2 + y^2 - 10x + 6y + 14 = 0$

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locus (1 Viewer)

simDS

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ninetypercent

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