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  4. The number of tangents drawn to the curve x y=4 from point (0,1) is

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Q. The number of tangents drawn to the curve $x y=4$ from point $(0,1)$ is

Application of Derivatives

Solution:

Equation of tangent is $y-4 / h =-4 / h ^2( x - h )$
It passes through $(0,1) \Rightarrow 1-4 / h =4 h / h ^2$
$\Rightarrow h-4=4 \Rightarrow h=8$
$ \Rightarrow $ tangent is $y-1 / 2=-1 / 16(x-8) $.