Lines are drawn from a point P(-1, 3) to a ci | vedclass

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(B) The power of point $P(-1, 3)$ with respect to the circle $x^2 + y^2 - 2x + 4y - 8 = 0$ is given by $PA 	imes PB = (PT)^2$,where $PT$ is the lengt

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$8$

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(B) The power of point $P(-1, 3)$ with respect to the circle $x^2 + y^2 - 2x + 4y - 8 = 0$ is given by $PA 	imes PB = (PT)^2$,where $PT$ is the length of the tangent from $P$ to the circle.Calculating the power of the point:$(PT)^2 = (-1)^2 + (3)^2 - 2(-1) + 4(3) - 8$$(PT)^2 = 1 + 9 + 2 + 12 - 8 = 16$Thus,$PA 	imes PB = 16$.Using the Arithmetic Mean-Geometric Mean $(AM \geq GM)$ inequality for positive real numbers $PA$ and $PB$:$\frac{PA + PB}{2} \geq \sqrt{PA 	imes PB}$$PA + PB \geq 2 \sqrt{16}$$PA + PB \geq 2 	imes 4 = 8$The minimum value of $PA + PB$ is $8$.

Lines are drawn from a point $P(-1, 3)$ to a circle $x^2 + y^2 - 2x + 4y - 8 = 0$. If the line meets the circle at two points $A$ and $B$,then the minimum value of $PA + PB$ is:

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