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

Question

Aicharya · Accepted Answer

Equation of circle $ \begin{array}{ll} & x^2+y^2-8 x-2 y-8=0 \ \Rightarrow \quad & g=-4, f=-1, c=-8 \end{array} $ Centre $(4,1)$ and radius, $r=\sqrt{16+1+8}=5$ Distance from centre $(4,1)$ to the line $ \begin{aligned} & x+y+1=0 	ext { is } \ & \qquad\left|\frac{4+1+1}{\sqrt{2}}ight|=\frac{6}{\sqrt{2}}=3 \sqrt{2} \end{aligned} $ $ \begin{aligned} 	ext { Length of chord } & =2 \sqrt{(5)^2-(3 \sqrt{2})^2} \ & =2 \sqrt{25-18}=2 \sqrt{7} \end{aligned} $

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

Solution