Q. 94.8( 5 Votes )
Find the (i) lengths of the axes, (ii) coordinates of the vertices, (iii) coordinates of the foci, (iv) eccentricity and (v) length of the rectum of each of the following the hyperbola :
3y2 – x2 = 108
Answer :
Given Equation: 3y2 – x2 = 108 ⇒ 
Comparing with the equation of hyperbola 
we get,
a = 6 and b = 
(i) Length of Transverse axis = 2a = 12 units.
Length of Conjugate axis = 2b = 
units.
(ii) Coordinates of the vertices = (0, 
a) = (0, 
6)
(iv) Here, eccentricity, e = 
(iii) Coordinates of the foci = (0, 
ae) = (0, 
12)
(v) Length of the rectum = 
units.
Rate this question :
Find the equation of the hyperbola, the length of whose latus rectum is 4 and the eccentricity is 3.
RS Aggarwal - MathematicsFind the equation of the hyperbola whose foci are 
and the eccentricity is 
.
Find the equation of the hyperbola whose foci are (0, ±13) and the length of whose conjugate axis is 24.
RS Aggarwal - MathematicsFind the equation of the hyperbola whose vertices are (0, ±3) and the eccentricity is 
. Also, find the coordinates of its foci.
Find the equation of the hyperbola whose foci are 
and the length of the latus rectum is 8 units.
