Question

Find the axes, eccentricity, latus-rectum and the coordinates of the foci of the hyperbola 25x² – 36y² = 225.

Answer 1

Given:

The equation=> 25x² – 36y² = 225

The equation can be expressed as:

The obtained equation is of the form

Where, a = 3 and b = 5/2

Eccentricity is given by:

Foci: The coordinates of the foci are (±ae, 0)

(±ae, 0) = ±3 (√61/6) = ± √61/2

(±ae, 0) = (± √61/2, 0)

The equation of directrices is given as:

The length of latus-rectum is given as:

2b²/a

∴ Transverse axis = 6, conjugate axis = 5, e = √61/6, LR = 25/6, foci = (± √61/2, 0)