The exhaustive set of values of such that there exists a tangent to the ellipse such that the portion of the tangent intercepted by the hyperbola subtends a right angle at the centre of the curves is 

a) 
b) 
(1, 2] 

c) 
d) 
The exhaustive set of values of such that there exists a tangent to the ellipse such that the portion of the tangent intercepted by the hyperbola subtends a right angle at the centre of the curves is 

a) 
b) 
(1, 2] 

c) 
d) 
(a)
Equation of tangent at point is
(i)
Let it cut the hyperbola at points and
Homogenizing the hyperbola with the help of the above the equation, we get
This is a pair of straight lines and
Given
Coefficient of coefficient of
Now,
Solving, we get