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Topic: Analytical Geometry - Equations From Geometric Definitions
Replies: 2   Last Post: May 12, 2006 2:20 PM

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Posts: 6
Registered: 12/6/04
Analytical Geometry - Equations From Geometric Definitions
Posted: Mar 9, 2005 9:18 AM
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First, I'm teaching myself at home. This is not for classroom. Here's the problem.

Directions: Find a polynomial equation with integer coefficients for the set of coplanar points described. Tell whether or not the graph is a conic section and, if it is, tell which conic section.

1. For each point, its distance from the fixed point (-3,0) is twice its distance from the fixed point (3,0).

Solution: The square root of [(x+3) squared + (y-0) squared] = 2 times the square root of [(x-3) squared + (y-0) squared]
which equals

x squared + y squared - 10x + 9 = 0 The conic section is a circle.

I realized right away when the question was asked, which conic section it would be. I am struggling to grasp the equations and would appreciate it if you could go step by step through the problem so I see the work and can understand it piece by piece. I've reworked it several times and just can't get to it.

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