Question

If pair of tangents $PA$ and $PB$ are draw from point $P(2,3)$ to the circle $x^2+y^2+4x+2y+1=0$ area $PAOB$, $O$ is centre.

• A. $2\sqrt{7}$
• B. $\sqrt{7}$
• C. $4\sqrt{7}$
• D. $8\sqrt{2}$

Answer 1

The correct option is C $4\sqrt{7}$

REF.Image.

$x^2+y^2+4x+2y+1=0$

$\Rightarrow (x+2{)}^2+(y+1{)}^2=2^2$

$\Rightarrow$ coordinates of o(-2,1)

$\Rightarrow OP=\sqrt{4^2+4^2}=4\sqrt{2}$

$\because O{P}^2=P{A}^2+O{A}^2$

and OA = Radius = 2 units

$\Rightarrow$ PA = $2\sqrt{7}units$

$\Rightarrow$ Area of PAOB = 2$\times$ Area of __ $△POA$

$=2\times \frac{1}{2}\times PA\times OA$

$=2\times \frac{1}{2}\times 2\sqrt{7}\times 2$

$=4\sqrt{7}$ square units

(c)