HyperbolaHard

Question

The tangent to the hyperbola xy = c2 at the point P intersects the x-axis at T and the y-axis ′T′. The normal to the hyperbola at P intersects the x-axis at N and the y-axis at N′. The areas of the triangles PNT and PN ′T′ are ᐃ and ᐃ′  respectively, then is -

Options

A.equal to 1
B.depends on t
C.depends on c
D.equal to 2

Solution

       
Let point P be
Equation of tangent at P is
x + yt2 = 2ct
∴  T is (2ct, 0) & T′ is
Now equation of normal at P is
t2 x - y = ct3 - c/t
∴ N
ᐃ = =
ᐃ′ = c2 (1 + t4)
∴ .

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