Q. 54.1( 11 Votes )

# In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

5y^{2} – 9x^{2} = 36

Answer :

The given equation is 5y^{2} – 9x^{2} = 36

We can re-write the given as

Or ……….. (1)

On comparing this equation (1) with the standard equation of hyperbola

, we get,

a = and b =2

We know, a^{2} + b^{2} = c^{2}

Thus,

c^{2} = =

⇒ c =

Therefore,

The coordinates of the foci are

The coordinates of the vertices are .

Eccentricity, e =

Length of latus rectum =

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