CircleHardBloom L3
Question
A ray of light incident at the point $( - 2, - 1)$ gets reflected from the tangent at $(0, - 1)$ to the circle $x^{2} + y^{2} = 1$. The reflected ray touches the circle. The equation of the line along which the incident ray moves, is:
Options
A.$4x - 3y + 11 = 0$
B.$4x + 3y + 11 = 0$
C.$3x + 4y + 11 = 0$
D.$4x + 3y + 7 = 0$
Solution
Sol. [Key Concept: A ray reflecting off a tangent: reflect the incident point/line across the tangent line.]
$$tan2\theta = \frac{2\left( \frac{1}{2} \right)}{1 - \frac{1}{4}} = \frac{4}{3} $$Slope of $QR = - \frac{4}{3}$
∴ Equation of incident ray $QR$ is
$$\begin{matrix} y + 1 & \ = - \frac{4}{30}(x + \\ 3y + 4x + 11 & \ = 0 \end{matrix}$$
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