The length of the chord intercepted by the circle $x^2+y^2-6 x+8 y-5=0$ on the line $2 x-y=5$ is equal to units

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Aicharya · Accepted Answer

Centre $=(3,-4)$ $\text {Radius }=\sqrt{9+16+5}=\sqrt{30}$ $d=$ Perpendicular distance from $(3,-4)$ to the chord $2 x-y-5=0$ $\begin{aligned} d & =\frac{|2(3)-(-4)-5|}{\sqrt{4+1}} \ d & =\frac{|6+4-5|}{\sqrt{5}} \ d & =\sqrt{5} \ \text { length of chord } & =2 \sqrt{r^2-d^2}=2 \sqrt{30-5} \ & =2 \times 5=10 \text { units } \end{aligned}$ Hence, option (a) is correct.

The length of the chord intercepted by the circle \(x^2+y^2-6 x+8 y-5=0\) on the line \(2 x-y=5\) is equal…

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