Question

Tangents are drawn through the point $P(-2,-3)$ to touch the circle $x^2+y^2-2x-10y+1=0$. The length of line segment $PA$, $A$ being the point on the circle where the line meets the circle at coincident points, is

• A. $16$
• B. $4\sqrt{3}$
• C. $48$
• D. none of these

Answer 1

The correct option is B $4\sqrt{3}$

Lines are drawn through the point $P(-2,-3)$ to meet the circle $x^2+y^2-2x-10y+1=0$.
$A$ is the point on the circle where the line meets the circle at coincident points.
$\Rightarrow$ Line is tangent to the circle.
$\Rightarrow PA$ is length of tangent from $P$ to the circle.
$\sqrt{S_{11}}=\sqrt{4+9+4+30+1}=\sqrt{48}=4\sqrt{3}$
$\therefore PA=4\sqrt{3}$
Hence, option B.