From a point P(0, b) two tangents are drawn to the circle x^2+y^2=16 and these two tangents intersect X -axis is two points A and B . If the area of P A B is minimum, then the equation of its circumcircle is

Step-by-step solution

Equation of pair of tangents from point (0, b) drawn to the circle x^2+y^2=16 is For point A and B , put y=0 , then we are getting aligned & (x^2-16 ) (b^2-16 )=16^2 & x^2= 16 b^2 b^2-16 x= 4 b b^2-16 aligned So, x -coordinate of A and B is 4 b b^2-16 Now, area of P A B= = 1 2 b ( 8 b b^2-16 )= 4 b^2 b^2-16 Now, for minimum area d d b =0 aligned & & b^2-16 (8 b) & =4 b^2 b b^2-16 & & 8 (b^2-16 ) & =4 b^2 & & b^2 & =32 & & b & = 4 2 aligned So, x - coordinate of A and B is 16 2 4 = 4 2 So, P(0, 4 2 ), A(4 2 , 0) and