The length of the chord intercepted by the ci | vedclass

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(D) The equation of the circle is $x^2+y^2-4x+4y+3=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2, f=2, c=3$. The center of the circle is $C(-g

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$2\sqrt{10}$

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(D) The equation of the circle is $x^2+y^2-4x+4y+3=0$. Comparing with $x^2+y^2+2gx+2fy+c=0$,we get $g=-2, f=2, c=3$. The center of the circle is $C(-g, -f) = (2, -2)$ and the radius $r = \sqrt{g^2+f^2-c} = \sqrt{(-2)^2+2^2-3} = \sqrt{4+4-3} = \sqrt{5}$. The line equation is $x-3y-13=0$. The perpendicular distance $d$ from the center $(2, -2)$ to the line $x-3y-13=0$ is $d = \frac{|(1)(2) - 3(-2) - 13|}{\sqrt{1^2+(-3)^2}} = \frac{|2+6-13|}{\sqrt{10}} = \frac{|-5|}{\sqrt{10}} = \frac{5}{\sqrt{10}} = \frac{\sqrt{10}}{2}$. The length of the chord is $2\sqrt{r^2-d^2} = 2\sqrt{5 - \frac{10}{4}} = 2\sqrt{5 - 2.5} = 2\sqrt{2.5} = 2\sqrt{\frac{5}{2}} = 2 \cdot \frac{\sqrt{5}}{\sqrt{2}} = \sqrt{2} \cdot \sqrt{5} = \sqrt{10}$.

The length of the chord intercepted by the circle $x^2+y^2-4x+4y+3=0$ on the line $x=3y+13$ is units.

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