Ellipse Flashcards
What is the standard equation of an ellipse?
x^/a^ + y^/b^= 1
Where b^=a^(1-e^)
How do you prepare the equation of an ellipse?
If s is the focus , e is the eccentricity, and P is any point on the ellipse , then
SP/PM =e
What is latus rectum ?
Latus rectum is a double ordinate passing through the focus.
What is focal distance ?
Focal distance is the distance of any point on the ellipse from its foci.
For a>b , what are the coordinate of verties of ellipse ?
(a,0) and (-a,0)
For a>b , what are the coordinate of foci of ellipse ?
(ae,0) and (-ae,0)
For a>b , what are the lengths of major axis and minor axis ?
Length of major axis is 2a (eq y=0)and length of minor axis is 2b(eq x=0)
For a>b , what is the equation of directrices ?
x= a/e and x=-a/e
For a>b , what is the eccentricity of ellipse ?
e= [1-b^/a^]^1/2
For a>b , what is the length of latus rectum ?
2b^/a
For a>b , what is the focal distance of point (x,y)
a+ex and a-ex
For b>a, what is the length of major axis and minor axis ?
Length of major axis is 2b and length of minor axis is 2a
For b>a, what is the length of latus rectum ?
Length of latus rectum is 2a^/b
The sum of focal distances of any two points on an ellipse is equal to what?
Major axis.
S’P+SP=2a
What is an auxiliary circle ?
Circle described on the major axis as diameter is called auxiliary circle.
x^+y^=a^.
x= a cos # and y= b sin # satisfied the equation of the ellipse.