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10-1.Circle and System of Circles
medium
If a line passing through origin touches the circle ${(x - 4)^2} + {(y + 5)^2} = 25$, then its slope should be
A
$ \pm \frac{3}{4}$
B
$0$
C
$ \pm \,3$
D
$ \pm \,1$
Solution
(b) Let equation of line be $y = mx$ or $y – mx = 0$
Then applying condition for tangency,
$\left| {\frac{{ – 5 – 4m}}{{\sqrt {1 + {m^2}} }}} \right| = 5 $
$\Rightarrow 25 + 16{m^2} + 40m = 25 + 25{m^2}$
$ \Rightarrow 9{m^2} – 40m = 0 \Rightarrow m = 0$ or $m = \frac{{40}}{9}$.
Standard 11
Mathematics
