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If tangents drawn from the point (a ,2) ...

If tangents drawn from the point `(a ,2)` to the hyperbola `(x^2)/(16)-(y^2)/9=1` are perpendicular, then the value of `a^2` is _____

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The correct Answer is:
3
Since tangents drawn from the point `A(a,2)` are perpendiular, A must lie on the director circle `x^(2)+y^(2)=7`. Putting y = 2, we get `x^(2)=a^(2)=3.`
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