Q3 of 71 Page 27

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

9x2 – 16y2 = 144

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,





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 3

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

16x2 – 9y2 = -144

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

4x2 – 3y2 = 36