Question

Let the tangents drawn to the circle x²+y²=16 from the point P(0,h) meet the x-axis at point A and B. If the area of triangle APB is minimum, then h equals to?

Answer 1

Equation of tangent of m slope to circle x²+y²=16 is

Hence equation tangents are

[Take h>0 as it does not effect result]

As maximum value of area will tend towards infinite, then h=±4√2 must give minima, 

hence h=±4√2

Comments

thanks.....#anukriti

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While writing equation of tangent y=√(h^2-16)/4 x+h/4 instead of h/4 it should be h
Since h/4 has no impact on answer as it gets vanished further you may have not noticed the error

Answer 2

Given circle is x2+y2=16 and tangents are drawn from P(0,h) such that they intersect x-axis at A and B
Area of ΔAPB is minimum, only when it is a right angled triangle with right angle at P.
∴  Equations of AP and BP are x+y−h=0 and x−y+h=0 respectively
As AP is tangent to the circle distance from origin to x+y−h=0 is equal to radius.
⇒h√2=4
∴h=4√2