# Math (Analytic Geometry)

1. Find the equation of the set of all points P(x,y) that is equidistant from (-3,0) and (3,-5).

2. Find the equation of the set of all points P(x,y) that is twice as far from (-8,8) as from (-2,2).

3. Find the equation of the set of all points P(x,y) such that the sum of the distance from (-4,0) and (4,0) is equal to 12.

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1. Assuming you just want verification of your results,

1. y + 5/2 = 6/5 x

2. (x+8)^2+(y-8)^2 = 4((x+2)^2+(y-2)^2)
or, x^2+y^2 = 32

3. Clearly this is the ellipse with foci at the two points, and a=6, c=4, b^2=20

x^2/36 + y^2/20 = 1

see http://www.wolframalpha.com/input/?i=ellipse+x%5E2%2F36+%2B+y%5E2%2F20+%3D+1

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