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. 4x 2 – 3y 2 = 36

Philoid · Accepted Answer

Given: 4x² – 3y² = 36

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 are given by (±ae, 0)

The equation of directrix are

Length of latus rectum is

Here, a = 3 and b =

Therefore,

The equation of directrix are:

Length of latus rectum,

= 8