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Example:
Show that the line 4x – 3y = 9 touches the hyperbola 4x2 – 9y2 = 27.
Solution:
We know that if the line y = mx + c touches the hyperbola x2/a2–y2/b2 = 1, then c2= a2m2 – b2
or a2m2 – b2 = c2
Hence the given line touches the given hyperbola.
⇒ ß = π – α Hence proved.
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