The number of points outside the hyperbola x216+y225=1 from where two ⊥ tangents can be drawn to the hyperbola is/are
A
0
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B
1
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C
3
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D
Infinitely many points
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Solution
The correct option is A0 Def: The director circle of a hyperbola is the locus of points from which ⊥ tangent are drawn to the given hyperbolar. Equation of director circle of x2a2+y2b2=1 is given by x2+y2=a2−b2=16−25=−9 which is impossible ∴ no point exist outside the hyperbola x216+y225=1