Question -
Answer -
(i) 4x2 + 9y2 = 1
Given:
The equation of ellipse => 4x2 + 9y2 =1
This equation can be expressed as
By using the formula,
Eccentricity:
Here, a2 = ¼, b2 = 1/9
Length of latus rectum = 2b2/a
= [2 (1/9)] / (1/2)
= 4/9
Coordinates of foci (±ae, 0)
(ii) 5x2 + 4y2 = 1
Given:
The equation of ellipse => 5x2 + 4y2 =1
This equation can be expressed as
By using the formula,
Eccentricity:
Here, a2 = 1/5 and b2 = ¼
Length of latus rectum = 2b2/a
= [2(1/5)] / (1/2)
= 4/5
Coordinates of foci (±ae, 0)
(iii) 4x2 + 3y2 = 1
Given:
The equation of ellipse => 4x2 + 3y2 =1
This equation can be expressed as
By using the formula,
Eccentricity:
Here, a2 = 1/4 and b2 = 1/3
Length of latus rectum = 2b2/a
= [2(1/4)] / (1/√3)
= √3/2
Coordinates of foci (±ae, 0)
(iv) 25x2 + 16y2 = 1600
Given:
The equation of ellipse => 25x2 + 16y2 =1600
This equation can be expressed as
By using the formula,
Eccentricity:
Here, a2 = 64 and b2 = 100
Length of latus rectum = 2b2/a
= [2(64)] / (100)
= 32/25
Coordinates of foci (±ae, 0)
(v) 9x2 + 25y2 = 225
Given:
The equation of ellipse => 9x2 + 25y2 =225
This equation can be expressed as
By using the formula,
Eccentricity:
Here, a2 = 25 and b2 = 9
Length of latus rectum = 2b2/a
= [2(9)] / (5)
= 18/5
Coordinates of foci (±ae, 0)
