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 \Delta APB is minimum, then   h  is equal to :

  • Option 1)

    4\sqrt{3}

  • Option 2)

    3\sqrt{3}

  • Option 3)

    3\sqrt{2}

  • Option 4)

    4\sqrt{2}

 

Answers (1)

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.

-

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)

4\sqrt{3}

Incorrect option    

Option 2)

3\sqrt{3}

Incorrect option    

Option 3)

3\sqrt{2}

Incorrect option    

Option 4)

4\sqrt{2}

Correct option

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