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10-1.Circle and System of Circles
normal
Consider circle $S$ : $x^2 + y^2 = 1$ and $P(0, -1)$ on it. $A$ ray of light gets reflected from tangent to $S$ at $P$ from the point with abscissa $-3$ and becomes tangent to the circle $S.$ Equation of reflected ray is
A
$3x + 4y -5 = 0$
B
$-3x + 4y + 5 = 0$
C
$3x -4y + 5 = 0$
D
$3x -4y -5 = 0$
Solution
$\mathrm{y}+1=\mathrm{m}(\mathrm{x}+3)$
$\Rightarrow \mathrm{mx}-\mathrm{y}+3 \mathrm{x}-1=0$
Distance from $(0,0)=1$
$\Rightarrow\left|\frac{3 m-1}{\sqrt{1+m^{2}}}\right|=1 \Rightarrow m=0$ or $\frac{3}{4}$
$\therefore $ Reflected ray $: 3 x-4 y+5=0$
Standard 11
Mathematics
