Question

2.4 25

Answer 1

The given equation of ellipse is

x 2 4 + y 2 25 =1 (1)

Since the denominator of y 2 25 is greater than the denominator of x 2 4 , major axis is y axis.

Therefore, the equation of ellipse is represented as

x 2 b 2 + y 2 a 2 =1 (2)

where c= a 2 − b 2 .(3)

Here, a=5 and b=2

Now substitute value of a and b in (3)

c= a 2 − b 2 c= 25−4 c= 21

Since major axis is y axis, coordinates of foci are (0,±c)=(0,± 21 )

Since major axis is y axis, coordinates of vertices are (0,±a)=(0,±5)

Length of major axis = 2a =2×5 =10

Length of minor axis = 2b =2×2 =4

Eccentricity e= c a = 21 5

Length of latus rectum = 2 b 2 a = 2× 2 2 5 = 2×4 5 = 8 5

Thus, the equation x 2 4 + y 2 25 =1 has foci (0, 21 ) and (0,− 21 ) , vertices (0,5) and (0,−5) , length of major axis 10, length of minor axis 4, eccentricity 21 5 and length of latus rectum 8 5