Question

5.49 36

Answer 1

The given equation of ellipse is

x 2 49 + y 2 36 =1 (1)

Since the denominator of x 2 49 is greater than the denominator of y 2 36 , major axis is x axis.

Therefore, the equation of ellipse is represented as

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

where, a is the length of semi major axis, b is the length of semi minor axis,and c is the distance of the focus from the center of the ellipse which is given as,

c= a 2 − b 2 (3)

By comparing this equation of ellipse with the given equation of ellipse, we get , a=7 and b=6

By substituting the value of a and b in (3) , we get

c= a 2 − b 2 c= 49−36 c= 13

Since major axis is x axis, coordinates of foci are (±c,0)=(± 13 ,0)

Since major axis is x axis, coordinates of vertices are (±a,0)=(±7,0)

Length of major axis = 2a =2×7 =14

Length of minor axis = 2b =2×6 =12

Eccentricity e= c a = 13 7

Length of latus rectum = 2 b 2 a = 2× 6 2 7 = 2×36 7 = 72 7

Thus, the equation x 2 49 + y 2 36 =1 has foci (± 13 ,0) , vertices (±7,0) , length of major axis 14, length of minor axis 12, eccentricity 13 7 and length of latus rectum 72 7