Find the graph and all the characteristics (centre, vertex, covertice, length of minor and major axis, length of latus rectum, equation of directrices and latus
rectum) of the graph with equation 8x^2 + 3y^2 = 24.

The given equation is 16x

2

+y

2

=16

It can be written as

16x

2

+y

2

=16

1

x

2

+

16

y

2

=1

1

2

x

2

+

4

2

y

2

=1...(1)

Herethe denominator of

4

2

y

2

is greater than the denominator of

1

2

x

2

Therefore, the major axis is along the y-axis while the minor axis is along the x-axis.

On comparing equation (1) with

b

2

x

2

+

a

2

y

2

=1, we obtain b=1 and a=4

∴ae=c=

a

2

−b

2

=

16−1

=

15

Therefore, the coordinates of the foci are (0,±

15

)

The coordinates of the vertices are (0,±4)

Length of major axis =2a=8

Length of minor axis =2b=2

Eccentricity e=

a

c

=

4

15

Length of latus rectum =

a

2b

2

=

4

2×1

=

2

1

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