Q2 of 70 Page 262

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

The given equation is or

On comparing this equation with the standard equation of hyperbola


, we get,


a = 4 and b =,


We know, a2 + b2 = c2


Thus,


c2 = 32 + = 36


⇒ c = 6


Therefore,


The coordinates of the foci are (0, 6).


The coordinates of the vertices are (0, 3).


Eccentricity, e =


Length of latus rectum =


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20

In each of the following, find the equation for the ellipse that satisfies the given conditions:

Major axis on the x-axis and passes through the points (4,3) and (6,2).

 1

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

 3

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

9y2 – 4x2 = 36

 4

In each of the, find the coordinates of the foci and the vertices, the eccentricity and the length of the latus rectum of the hyperbolas.

16x2 – 9y2 = 576