Question

Let $x^2+y^2-4x-2y-11=0$ be a circle. A pair of tangents from the point $(4,5)$ with a pair of radii form a quadrilateral of area sq. units.

Answer 1

The equation of circle is, $(x-2{)}^2+(y-1{)}^2-16=0.$
radius $r=4$ units

$AD=L=\sqrt{S_1}\Rightarrow L=\sqrt{2^2+4^2-16}=2$
Hence area of $ABCD=L\cdot r=8$ sq. units