Question

Factorize: (25/9) x2 – y2/16​

Answer 1

Answer:

Equation of ellipse is

25

x

2

+

16

y

2

=1,a>b and

equation of hyperbola is

25

x

2

+

16

y

2

=1,a>b Let e

Let e' be the eccentricities of the ellipse and hyperbola.

∴e=

a

2

a

2

−b

2

=

25

25−16

=

5

3

and e

′

=

a

2

a

2

+b

2

=

25

25+16

=

5

41

(i) Centre of ellipse is (0,0) and centre of hyperbola is (0,0).

(ii) Foci of ellipse are (±ae,0) or (±15,0) foci of hyperbola are (±ae

′

,0) or (±

41

,0)

(iii) Directrices of ellipse are x=±

e

a

⇒x=±

3

25

directrices of hyperbola are

x=±

e

a

⇒x=±

41

25

(iv) Vertices of ellipse are (±a,0) or (±5,0) Vertices of hyperbola are (±a,0) or (±5,0)

From the above discussions, their are common in centre and vertices.