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Point P(x,y) moves so that the midpoint between P and the origin is always a point on...

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tamanim | Student, Grade 11 | (Level 2) Honors

Posted September 7, 2013 at 12:05 AM via web

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Point P(x,y) moves so that the midpoint between P and the origin is always a point on the circle x^2 + y^2 = 1. Find the equation of the locus of P.

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embizze | High School Teacher | (Level 1) Educator Emeritus

Posted September 7, 2013 at 1:05 AM (Answer #1)

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The point P(x,y) moves so that the midpoint of `bar(OP)` lies on the circle `x^2+y^2=1` . Find the equation for the locus for P:

`x^2+y^2=1` is a circle centered at the origin with radius 1.

P defines a dilation centered at the origin with scale factor 2. Thus the locus of P is the circle centered at the origin with radius 2.

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The locus of P is given by `x^2+y^2=4`

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