Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus-rectum of the hyperbola.

Question

Find the eccentricity, coordinates of the foci, equations of directrices and length of the latus-rectum of the hyperbola. 16x 2 – 9y 2 = -144

Philoid · Accepted Answer

Given: 16x² – 9y² = -144

To find: eccentricity(e), coordinates of the foci f(m,n), equation of directrix, length of latus-rectum of hyperbola.

Formula used:

For hyperbola

Eccentricity(e) is given by,

Foci is given by (0, ±be)

The equation of directrix are:

Length of latus rectum is

Here, a = 3 and b = 4

⇒ c = 5

Therefore,

Foci: (0, ±5)

The equation of directrix are:

Length of latus rectum,