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  • Find the length of the chord of the circle <img alt="\mathrm{(x - 3)^{2} + (y - 5)^{2} = 80" src="https://entrancecorner.oncodecogs.com/gif.latex?%5Cmathrm%7B%28x%20

Find the length of the chord of the circle \mathrm{(x - 3)^{2} + (y - 5)^{2} = 80 cut off by the line 3x − 4y − 9 = 0.

 

Option: 1

4


Option: 2

6


Option: 3

10


Option: 4

8


Answers (1)

best_answer

Length of the perpendicular from centre (3, 5) upon 3x − 4y − 9 = 0

\mathrm{=\left(\frac{9-20-9}{\sqrt{9+16}}\right)=\frac{20}{5}=4=p \text { (say) }}

Radius of the circle \mathrm{=\sqrt{80}=r(\text { say })}

∴ Length of the chord \mathrm{=2 \sqrt{r^2-p^2}}

                                   \mathrm{\begin{aligned} & =2 \sqrt{80-16}=2 \sqrt{64} \\ & =2 \times 8=16 . \end{aligned}}

Posted by

Kuldeep Maurya

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