SOLUTION: Find the equation of the set of all points (x,y) such that the absolute value of the difference between their distance to (-3,0) and to (3,0) is 4. Thanks

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Question 876297: Find the equation of the set of all points (x,y) such that the absolute value of the difference between their distance to (-3,0) and to (3,0) is 4.
Thanks
Answer by ewatrrr(24785) About Me  (Show Source):
You can put this solution on YOUR website!
A hyperbola may be defined equivalently as the locus of points where the absolute value of the difference of the distances to the two foci is a constant equal to 2a, the distance between its two vertices.
Standard Form of an Equation of an Ellipse is %28x-h%29%5E2%2Fa%5E2+%2B+%28y-k%29%5E2%2Fb%5E2+=+1+
absolute value of the difference between their distance to F(-3,0) and to F(3,0) is 4 = 2a
Standard Form of an Equation of an Hyperbola opening right and left is:%28x-h%29%5E2%2Fa%5E2+-+%28y-k%29%5E2%2Fb%5E2+=+1
%28x%29%5E2%2F2%5E2+%2B+%28y%29%5E2%2Fb%5E2+=+1+ C(0,0)
sqr(a^2 + b^2) =sqr(4+ b^2)= 3, b^2 = 5
%28x%29%5E2%2F4%2B+%28y%29%5E2%2F5+=+1+