Question

The foci of hyperbola coincides with foci of the ellipse x²/25+y²/9=1. Find the equation of hyperbola if it's eccentricity is 2.​

Answer 1

Answer:

The foci of the ellipse are also the foci of an hyperbola,

then we have, for the ellipse,

a

2

−c

2

=b

2

so 25−c

2

=9 and that means c

2

=16.

This ellipse has its major axis on the x-axis.

For the hyperbola, which must have its transverse axis on the x-axis, the equation

c

2

−a

2

=b

2

and

e=

a

c

=2.

Only the c value is the same as for the ellipse; c=4.

Thus

a

4

=2

tells us that a (for the hyperbola) =2.

Therefore we compute b

2

=16−4=12.

The equation of the hyperbola is

a

2

x

2

−

b

2

y

2

=1 substituting gives us

4

x

2

−

12

y

2

=1

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