AP EAMCET Engineering 2018 Apr 22 Shift 2 Paper

Equation of pair of tangents from the point (0,b) drawn to the circle x2+y2=16 is,
(x2+y2−16)(b2−16)=(by+16)2
For point A and B, take y = 0,
So,
(x2−16)(b2−16)=162
x±

4b

√b2−16

Now,
For ∆PAB,
Δ=±

1

2

b(

8b

√b2−16

)
=

4b2

√b2−16

For minimum area

dΔ

db

=0,
√b2−16(8b)=4b2

b

√b2−16

b2=32
b=±4√2
So, P(0,±4√2),A(4√2,0) and B(−4√2,0)
Thus, the equation of the circumference of ∆PAB is
x2+y2=32