Table Of Standard Ellipse

Table of standard ellipse

Equation	x² /a² +y² / b² =1 when a > b c²= a² – b² TYPE 1 ↓	x² /b² +y² / a² =1 when a > b c²= a² – b² TYPE 2 ↓
Focus	(± C, 0)	(± C, 0)
Major axis	y= 0	x=0
Directrices	x = ± c / e²	y = ± c / e²
Vertices	(± a, 0)	(0, ± a)
Co vertices	(0, ± b)	(± b, 0)
Center	(0, 0)	(0, 0)
Eccentricity	e= c / a < 1	e= c / a < 1

Graph of an Ellipse Type 1 and 2

Let the equation of the ellipse be

x² /a² +y² / b² =1

since only even powers of both x and y occur in the figure, The cure is symmetric with respect to

both the axis

From the figure, we note that

x² /a² ≤ 1 and y² / b² ≤ 1

that is

x² ≤ a² and y² ≤ b²

-a ≤ x ≤ a and -b ≤ x ≤ b

thus, all the points or within the rectangle. The curve meets the x-axis at A (-a, 0) and

it meets the y-axis at B(0, -b) B'(0, b)

The graph of the ellipse is

x² /b² +y² / a² =1 a > b

TABLE IMPORTANT NOTE STANDARD ELLIPSE

(1) each ellipse have length of major axis = 2a

(2) each ellipse of minor axis = 2b

(3) each ellipse length of Latusrectum = 2b² / a

(4) Foci lies on the major axis

Example:

Find an equation of ellipse having center at (0, 0) focus at (0, -3) and one vertex at (0,4)Example :

Solution:

length of the major axis is

a = 4

foci = F= 3

from b² = a² – c ²

b² = 16 – 9

b² = 7

b = √ 7 which is the length of semi minor axis

since the Foci lies on the y-axis equation

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