Question

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

9x² – 16y² = 144

Answer 1

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 \(\frac{x^2}{a^2} - \frac{y^2}{b^2} = 1\)

Eccentricity(e) is given by,

e = \(\frac{c}{a}\), Where C = \(\sqrt{a^2 + b^2}\)

Foci is given by (±ae, 0) 

Equation of directrix are: X = ± \(\frac{a}{e}\)

Length of latus rectum is \(\frac{2b^2}{a}\) 

Here, a = 4 and b = 3

Foci: (±5, 0) 

Equation of directrix are:

Length of latus rectum,