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Illustration:
Solution:
Any tangent to the conjugate hyperbola x2/a2–y2/b2 = –1 is
x = my + √b2m2–a2. …… (2)
If this is same as the chord (1), then m = a2y1/b2x1 and hence
a4/x12 [x12/a2 – y12/b2]2 = b2m2 – a2 = b2a4y12/b4x12 – a2
Or [x12/a2 – y12/b2]2 = y12/b2 – x12/a2 or x12/a2 – y12/b2 = –1
⇒ (x1, y1) lies on the conjugate hyperbola.
⇒ the chord (1) touches conjugate hyperbola and is bisected at the point of contact.
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