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Andrew
Posts:
6
Registered:
12/6/04
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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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