Question:
The eccentricity of the ellipse 9x2 + 25y2 – 18x – 100y – 116 = 0, is
The eccentricity of the ellipse 9x2 + 25y2 – 18x – 100y – 116 = 0, is
Options:
- 25/16
- 4/5
- 5/4
- 16/25
- 25/16
- 4/5
- 5/4
- 16/25
Correct Answer: b)
Explanation:
9×2 +25y2 – 18x – 100y – 116 = 0
‘ = 90% – 2x) + 25(y2 – dy) = 116
= 9×2 -2x + 1) + 25(y% – dy + 4) = 116 + 100 +9
1 = 9(x- 12 +25(y-2)% =25
91)? 25(y—2)°
i = el + od =1
2 2
1 = i) + Co) =1 \
Lo
1 Comparing it with = + x =1, we get
a?=25andb>=9
‘ a=5andb=3 i
1 Here, a > b, so the major and the minor axes of the ellipse are along the x-axis and y-axis,
hon a
‘ respecti√ely. ‘
— 1 ¥
) Now, e = 4/1 =
_ / 9
H =e=,/1— %
i Se=,/p i
1 M
>e=3
) 66. H
@y=0
‘
9×2 +25y2 – 18x – 100y – 116 = 0
‘ = 90% – 2x) + 25(y2 – dy) = 116
= 9×2 -2x + 1) + 25(y% – dy + 4) = 116 + 100 +9
1 = 9(x- 12 +25(y-2)% =25
91)? 25(y—2)°
i = el + od =1
2 2
1 = i) + Co) =1 \
Lo
1 Comparing it with = + x =1, we get
a?=25andb>=9
‘ a=5andb=3 i
1 Here, a > b, so the major and the minor axes of the ellipse are along the x-axis and y-axis,
hon a
‘ respecti√ely. ‘
— 1 ¥
) Now, e = 4/1 =
_ / 9
H =e=,/1— %
i Se=,/p i
1 M
>e=3
) 66. H
@y=0
‘