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Q.
The length of the chord joining the points in which the straight line
$ \frac {x}{3}+\frac {y}{4}=1 $ circle $ x^2 + y^2 $ = $ \frac {169}{25} $
AMUAMU 2019
Solution:
We have, equations of line and circle are
$\frac{x}{3}+\frac{y}{4}=1 ....$(i)
and $\Rightarrow 25 x^{2}+25 y^{2}=169 ....$(ii)
$\therefore$ Length of the perpendicular from centre $(0,0)$ of circle to the line (i) $=12 / 5$ and radius of the circle $=13 / 5$
$\therefore$ Required length $=2 \sqrt{\frac{169}{25}-\frac{144}{25}}=2$
