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

Find the length of the chord intercepted by the ci – Class 12 Mathematics

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x^2 + y^2 - 8x - 2y - 8 = 0

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Find the circle's centre and radius, the perpendicular distance from the centre to the line, then use $2\sqrt{r^2-d^2}$ .

The circle $x^2+y^2-8x-2y-8=0$ has centre $(4,1)$ and radius

$r=\sqrt{4^2+1^2+8}=\sqrt{16+1+8}=\sqrt{25}=5.$

The perpendicular distance from $(4,1)$ to the line $x+y+1=0$ is

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