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. 9x 2 – 16y 2 = 144

Philoid · Accepted Answer

Given: 9x² – 16y² = 144

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

9x² – 16y² = 144

Formula used:

For hyperbola

Eccentricity(e) is given by,

Foci is given by (±ae, 0)

Equation of directrix are:

Length of latus rectum is

Here, a = 4 and b = 3

⇒ c = 5

Therefore,

Foci: (±5, 0)

Equation of directrix are:

Length of latus rectum,