A series of chords of the hyperbola 
, are tangents to the circle described on the line joining the foci as diameter. The locus of their poles w.r.t. the hyperbola is
Text Solution
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Equation of the hyperbola is 
... (1)
Its foci are (ae, 0) and (- ae, 0).
Equation of the circle on the join of foci as diameter is
(x - ae) (x + ae) + (y - 0) (y - 0) = 0
or x 2 + y 2 = a 2 e 2 ... (2)
Let (x 1 , y 1 ) be the pole of a chord of (1).
Equation of chord i.e. polar of (x 1 , y 1 ) w.r.t. (1) is 
. ... (3)
Since it touches the circle (2), the length of ⊥ ⊥ from the centre (0, 0) of (2) on (3) is equal to radius ae.
⇒ ⇒ 
or 
.
∴ ∴ Locus of (x 1 , y 1 ) is 
.
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