Question

lf the tangents $PA$ and $PB$ are drawn from the point $P(-1,2)$ to the circles $x^2+y^2+x-2y-3=0$ and $C$ is the centre of the circle, then the area of the quadrilateral P$ACB$ is

• A. $4$
• B. $16$
• C. does not exist
• D. $12$

Answer 1

Answer: (C)

does not exist

PA = length of tangent from exterior point
$\therefore PA=PB=\sqrt{s_1}$
$\sqrt{1+4-1-4-3}$
$\sqrt{-3}$
Area of Quadrilateral $PBCA=area\Delta PAC+area\Delta PBC$
$=\frac{1}{2}\times PA\times r+\frac{1}{2}\times PB\times r$
$\frac{r}{2}\left[\sqrt{s_1=\sqrt{s_1}}\right]$
$r\sqrt{s_1}$
$r\sqrt{-3}$
area does not exist.