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Last Updated On [03-11-2023]

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)


Question ID - 56002 :-

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)

1 Answer
5876 Votes
3537

Answer Key : (a) -

(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



Next Question :

If  and  are four con-cyclic points on the rectangular hyperbola , then coordinates of the orthocentre of the triangle  is

a)

b)

c)

d)


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