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Q.
Which of the following equations of a line intercepts on the circle $x^{2}+y^{2}-6x-8y=0$ a chord of longest length?
NTA AbhyasNTA Abhyas 2022
Solution:
The chord nearest to the centre of the circle will be the longest chord.
From options, we see that the given lines are at a distance of $\frac{1}{\sqrt{2}},\frac{7}{\sqrt{2}},\frac{5}{\sqrt{2}},\frac{23}{5}$ respectively from the centre $\left(3,4\right)$ .
Hence, $\left(A\right)$ is correct