Q3 of 71 Page 27

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

2x2 – 3y2 = 5

Given: 2x2 – 3y2 = 5


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 = and b =







Therefore,






The 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.

4x2 – 3y2 = 36

 3

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

3x2 – y2 = 4

 4

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

 5

Find the centre, eccentricity, foci and directions of the hyperbola

16x2 – 9y2 + 32x + 36y – 164 = 0