The length of the chord intercepted by the ci | vedclass

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(C) The equation of the circle is $x^2+y^2+2x+4y-20=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=1, f=2, c=-20$. The center of the circle is $C(

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$\frac{8}{5} \sqrt{21}$

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(C) The equation of the circle is $x^2+y^2+2x+4y-20=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=1, f=2, c=-20$. The center of the circle is $C(-g, -f) = (-1, -2)$ and the radius $r = \sqrt{g^2+f^2-c} = \sqrt{1^2+2^2-(-20)} = \sqrt{25} = 5$. The perpendicular distance $d$ from the center $(-1, -2)$ to the line $3x+4y-6=0$ is given by $d = \frac{|3(-1)+4(-2)-6|}{\sqrt{3^2+4^2}} = \frac{|-3-8-6|}{5} = \frac{17}{5}$. The length of the chord is $2\sqrt{r^2-d^2} = 2\sqrt{5^2 - (\frac{17}{5})^2} = 2\sqrt{25 - \frac{289}{25}} = 2\sqrt{\frac{625-289}{25}} = 2\sqrt{\frac{336}{25}} = 2 	imes \frac{\sqrt{16 	imes 21}}{5} = 2 	imes \frac{4\sqrt{21}}{5} = \frac{8}{5}\sqrt{21}$.

The length of the chord intercepted by the circle $x^2+y^2+2x+4y-20=0$ on the line $3x+4y-6=0$ is

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