UPSC NDA Math Model Paper 1

Given: Equation of ellipse is 9x2+4y2=36
The given equation of ellipse can be re-written as

x2

4

+

y2

9

=1
As we can see that, the given ellipse is a vertical ellipse.
So, by comparing the equation

x2

4

+

y2

9

=1 with

x2

b2

+

y2

a2

=1 we get
⇒a2=9 and b2=4
As we know that, eccentricity of ellipse is given by e=√1−

b2

a2

⇒e=√1−

4

9

=

√5

3

As we know that, for a vertical ellipse equation of directrix is given by y=±

9

√5

So, the distance between the directrices is given by

2a

e

=

18

√5