COMEDK 2023 Shift 1 Paper

To find the eccentricity of the ellipse, we start with the given information that the length of the major axis of an ellipse is 3 times the length of the minor axis. First, let's define the standard notation for an ellipse and apply the given information.
The standard form of the ellipse with the major and minor axes along the x-axis and y-axis respectively is
‌

x2

a2

+‌

y2

b2

=1
where a is the semi-major axis and b is the semi-minor axis. The length of the major axis is 2a and the length of the minor axis is 2b. Given that the length of the major axis is 3 times the length of the minor axis, we have:
2a=3(2b)
a=3b
The eccentricity e of an ellipse is given by the formula:
e=√1−‌

b2

a2

Substitute a=3b into the eccentricity formula:
‌e=√1−‌

b2

(3b)2

‌e=√1−‌

b2

9b2

‌e=√1−‌

1

9

‌e=√‌

8

9

‌e=‌

√8

3

e=‌

2√2

3

Therefore, the correct answer is
Option B
‌

2√2

3