Numerical : Find the coordinates of the foci and the vertices , the eccentricity , the length of the latus rectum of the hyperbolas : x 2 / 9 – y 2 / 16 = 1
Solution : Comparing the equation x 2 / 9 – y 2 / 16 = 1 , with standard equation x 2 / a 2 – y 2 / b 2 = 1 , we get a = 3 & b = 4 .
c = √ ( a 2 + b 2 ) = √ ( 9 + 16 ) = 5
Therefore , the coordinates of the foci are (± 5 , 0 ) and that of vertices are (± 3 , 0 ). Also ,
The eccentricity e = c / a = 5 / 3 The latus rectum = 2b2 / a = 2 *( 4 ) 2 / 3 = 32 / 3