The length of the chord intercepted by the ci | vedclass

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(C) The given equation of the circle is $x^2+y^2-8x-2y-8=0$. Comparing this with the general form $x^2+y^2+2gx+2fy+c=0$,we get $g=-4$,$f=-1$,and $c=-8

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$2\sqrt{7}$

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(C) The given equation of the circle is $x^2+y^2-8x-2y-8=0$. Comparing this with the general form $x^2+y^2+2gx+2fy+c=0$,we get $g=-4$,$f=-1$,and $c=-8$. The centre of the circle is $(-g, -f) = (4, 1)$ and the radius $r$ is $\sqrt{g^2+f^2-c} = \sqrt{16+1+8} = \sqrt{25} = 5$. The perpendicular distance $d$ from the centre $(4, 1)$ to the line $x+y+1=0$ is given by: $d = \left|\frac{4+1+1}{\sqrt{1^2+1^2}}\right| = \frac{6}{\sqrt{2}} = 3\sqrt{2}$. The length of the chord is given by $2\sqrt{r^2-d^2}$. Length $= 2\sqrt{5^2 - (3\sqrt{2})^2} = 2\sqrt{25 - 18} = 2\sqrt{7}$ units.

The length of the chord intercepted by the circle $x^2+y^2-8x-2y-8=0$ on the line $x+y+1=0$ is:

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