Q3 of 71 Page 27

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

4x2 – 3y2 = 36

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


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9x2 – 16y2 = 144

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16x2 – 9y2 = -144

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3x2 – y2 = 4

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

2x2 – 3y2 = 5