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