SOLUTION: Find the polynomial equation with integer coefficients for the set of coplanar points described.
For each point,its distance from the fixed point (-3,0) is twice its distance fr
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Question 558641: Find the polynomial equation with integer coefficients for the set of coplanar points described.
For each point,its distance from the fixed point (-3,0) is twice its distance from the fixed point (3,0)
Answer by solver91311(24713) (Show Source): You can put this solution on YOUR website!
Let )
be a point on the desired locus.
The distance from any point to the point )
is given by the distance formula:
)^2\ +\ (y\ -\ 0)^2}\ \ =\ \sqrt{(x\ +\ 3)^2\ +\ y^2})
Similarly, the distance from any point to the point )
is given by:
^2\ +\ (y\ -\ 0)^2}\ \ =\ \sqrt{(x\ -\ 3)^2\ +\ y^2})
But we are also given that 
so:
^2\ +\ y^2}\ =\ 2\sqrt{(x\ -\ 3)^2\ +\ y^2})
Square both sides:
^2\ +\ y^2\ =\ 4\left((x\ -\ 3)^2\ +\ y^2\right))
All you need to do is simplify, collect like terms, put everything of value on the left and a zero on the right and you are done.
John
My calculator said it, I believe it, that settles it
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