# Let the tangents drawn to the circle, x2+y2=16 from the point P(0, h) meet the x-axis at points A and B.  If the area of is minimum, then   h  is equal to : Option 1) Option 2) Option 3) Option 4)

As we learnt in

Maxima Minima -

A functions graph follow up and down along x-axis then upper part is known as maxima and lower part is known as minima.

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Let equation of tangent is

$(y-h)=M(x-0)$

$\therefore y=Mx-h$

$\therefore h=\pm\sqrt{1+M^{2}}$

$\therefore AB=\pm\frac{4\sqrt{1+M^{2}}}{M}$

$\therefore Area =\frac{1}{2}\times AB\times OP$

$=\frac{1}{2}\times \frac{8\sqrt{1+M^{2}}}{M}\times 4\sqrt{1+M^{2}}$

$\frac{dA}{dm}=0$                    $\therefore m = 1$

$\therefore h=4\sqrt{1+1}$$=4\sqrt{2}$

Option 1)

Incorrect option

Option 2)

Incorrect option

Option 3)

Incorrect option

Option 4)

Correct option

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