MC 1 Chapter 1: ANALYTIC GEOMETRY: ELLIPSE

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5 Nov 2021
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Page 1 of 3: the sum of the distances from any point on the ellipse to the two foci is constant. Derive the equation of an ellipse with center , foci , and vertices. Major axis: horizontal ( -axis) the vertex point , we can calculate this constant sum: Using the figure above, the distance from to is ___________________ and the distance from to is ___________________. Thus, the sum of the two distances is ___________________________________: now, if you let be any point on the ellipse, the sum of the distances between and the two foci must also be equal to this distance . With some clever moving of terms around, we get: After factoring out some common factors, we get: Activity: now set the sum of the distances between and the two foci (found in part 2) equal to _____: