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If tangents drawn from the point \mathrm{A(c, 4)}  to the hyperbola \mathrm{\frac{x^2}{81}-\frac{y^2}{49}=1}  are perpendicular, then the value of \mathrm{c^2} is

Option: 1

14


Option: 2

16


Option: 3

15


Option: 4

None of these


Answers (1)

best_answer

Since tangents drawn from the point \mathrm{A(c, 4)} are perpendicular, A must lie on the director circle \mathrm{x^2+y^2=32}. Putting \mathrm{y=4}, we get \mathrm{x^2=c^2=16}

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