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**preview**shows half of the first page. to view the full**1 pages of the document.**10.5 Parametric Equations & Polar Coordinates

Conic Sections

Question #7 (Medium): Forming the Equation of Ellipse

Strategy

Sample Question

Find an equation for the conic that satisfies the given conditions.

Ellipse with foci at , and vertex at

Solution

Looking at the foci points, they are aligned at along a vertical line. Thus the ellipse stretch is

greater vertically. Then the ellipse equation follows the form of

with foci at

and vertices . Since the vertex is at , . Since the foci are at ,

the distance between these two foci represents . Thus , then . Then the value is the

midpoint between these two foci points. Thus . Then the vertices being , one of

the vertex given tells what the a value is. . Then working backwards with c and a based on

, , thus

Therefore the equation of the ellipse is

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