Question

x2
a2
2
2. Prove that for the ellipse
+
= 1, if x = asino,
b2
ds
V1 - e-sinad
do
ro​

Answer 1

Step-by-step explanation:

Given hyperbola is,

144

x

2

−

81

y

2

=

25

1

⇒

144/25

x

2

−

81/25

y

2

=1

⇒a

2

=

25

144

,b

2

=

25

81

,e=

1+

a

2

b

2

=

1+

144

81

=

12

15

∴ foci of hyperbola are (±ae,0)i.e(±3,0)

Now given ellipse is

16

x

2

+

b

2

y

2

=1

⇒a

2

=16

Assume eccentricity of this ellipse is e

′

then its foci are (±ae

′

,0)i.e(±4e

′

,0)

Given foci of given hyperbola and ellipse coincide

⇒4e

′

=3⇒e

′

=

4

3

For ellipse, using eccentricity relationship, e

′2

=1−

a

2

b

2

⇒

16

9

=1−

16

b

2

∴b

2

please give me brainliest

=7