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

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Question

$\mathrm{PA} 	imes \mathrm{PB}=(\mathrm{PT})^{2}$

where $\mathrm{PT}=$ length of tangent

$(\mathrm{PT})^{2}=(-1)^{2}+3^{2}-2(-1)+4(3)-8=16$

Vedclass · Accepted Answer

$8$

Vedclass · Answer

$\mathrm{PA} 	imes \mathrm{PB}=(\mathrm{PT})^{2}$

where $\mathrm{PT}=$ length of tangent

$(\mathrm{PT})^{2}=(-1)^{2}+3^{2}-2(-1)+4(3)-8=16$

$\mathrm{P}(\mathrm{A}) \mathrm{P}(\mathrm{B})=16$

$	herefore \mathrm{AM} \geq G M$

$P A+P B \geq 8$

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

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