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  • A ray of light incident at the point gets reflected from the tangent at <img alt="(0,-1)" src="https://entr

A ray of light incident at the point (-2,-1) gets reflected from the tangent at (0,-1) to the circle \mathrm{x^{2}+y^{2}=1}. The reflected ray touches the circle. The equation of the line aong which the incident ray moved is

Option: 1

\mathrm{4 x-3 y+11=0}


Option: 2

\mathrm{4 x+3 y+11=0}


Option: 3

\mathrm{3 x+4 y+11=0}


Option: 4

none of these


Answers (1)

best_answer

Any lnie through (-2,-1) is \mathrm{y+1=\mathrm{m}(\mathrm{x}+2)}. It touches the circle if

\mathrm{\left|\frac{2 \mathrm{~m}-1}{\sqrt{1+\mathrm{m}^{2}}}\right|=1 \Rightarrow \mathrm{m}=0,4 / 3}

Equation of the line PB is \mathrm{4 x-3 y+5=0}
Reflection of \mathrm{4 x-3 y+5=0}  in the line \mathrm{y+1=0} is

  \mathrm{\frac{4 x-3 y+5}{y+1}=\frac{2(0-3)}{1}=-6}

\mathrm{ \Rightarrow 4 x+3 y+11=0}

Posted by

Shailly goel

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