Question

find the area of the quadrilateral formed by a pair of tangents from the point (4,5) to the circle `x^2 + y^2 -4x -2y-11 = 0` and pair of its radii.

Answer 1

`C:x^2+y^2-4x-2y-11=0`
`(x-2)^2+(y-1)^2=4^2`
`PC=sqrt((4-2)^2+(5-1)^2)=sqrt21`
PA=2 units.
area of PACB=2 area of PAC
`=2*1/2*2*4`
`=8 unit^2`