Correct option (a),(c)
Explanation :
The eccentricity e of the ellipse is given by
16 = 25(1 - e2)
which gives that
e = 3/5
Hence, the eccentricity of the hyperbola is 5/3. Let
x2/α2 - y2/β2 = 1
be the hyperbola. Now,
β2 = α(25/9 - 1) = 16α2/9
This implies that the equation is
x2/α2 - 9y2/16α2 = 1
Also the hyperbola passes through the focus (3, 0) of the ellipse. This implies that
Hence, the equation of the hyperbola is
x2/9 - y2/16 = 1
One vertex is (3, 0) and the focus is