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Lecture

MAT136H1 Lecture Notes - Polar Coordinate System


Department
Mathematics
Course Code
MAT136H1
Professor
all

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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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