Question

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

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

Answer 1

The correct option is B

$4\sqrt{3}$

Explanation for the correct answer:

Length of tangent:

Given that: the point is $P(-2,-3)$

The equation of the circle is $x^2+y^2-2xy-10y+1=0$

Coincidental point means that $PA$ will be a tangent to the circle.

Length of the tangent $PA$:

$\mathbf{\text{Length of tangent}}\mathbf{}\mathbf{=}\sqrt{{\mathbf{S}}_{\mathbf{1}}}$

$$\begin{gathered} =\sqrt{{\left(-2\right)}^2+{\left(-3\right)}^2-2\left(-2\right)-10(-3)+1}\left[\because x=-2,y=-3\right] \\ =\sqrt{4+9+4+30+1} \\ =4\sqrt{3} \end{gathered}$$

Hence, the correct answer is option (B).