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Standard Equations of Ellipse

Equation of ellipse: 73432.png

a > b
73426.png
 
Center (0, 0)
Vertices a, 0)
Length of major axis 2a
Length of minor axis 2b
Foci (± ae, 0)
Equation of directrices x = ± a/e
Relation in ab, and e b2 = a2 (1 – e2)
Length of the rectum 73413.png
Ends of latus rectum 73401.png
Equation of auxiliary circle (circle described on major axis as diameter)
73388.png
 
Auxiliary circle is x2 + y2 = a2Q has coordinates (a cos φa sin φP is corresponding point on the ellipse which has coordinates (a cos φb sin φ)
Focal radii of any point P(x1y1) on ellipse SP = a – ex1 and SP = a + ex1
Sum of focal radii SP + SP 2a

b > a
73419.png
 
Center (0, 0)
Vertices (0, ± b)
Length of major axis 2b
Length of minor axis 2a
Foci (0, ± be)
Equation of directrices y = ± b/e
Relation in ab, and e a2 = b2 (1 – e2)
Length of the rectum 73407.png
Ends of latus rectum 73394.png
Equation of auxiliary circle (circle described on major axis as diameter)
73382.png
 
Auxiliary circle is x2 + y2b2Q has coordinates (b cos φb sin φP is corresponding point on the ellipse which has coordinates (a cos φb sin φ)
Focal radii of any point P(x1y1) on ellipse SP = b – ey1 and SP =b + ey1
Sum of focal radii SP + SP 2b




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