Question

A ray of light incident at the point (–2, –1) gets reflected from the tangent at (0, –1) to the circle x² + y² = 1. The reflected ray touches the circle. The equation of the line along which the incident ray moved is –

• A. 4x – 3y + 11 = 0
• B. 4x + 3y + 11 = 0
• C. 3x + 4y + 11 = 0
• D. None of these

Answer 1

Answer: (B)

4x + 3y + 11 = 0

Answer 2

Any line through P(–2, –1) is y + 1 = m(x + 2).

It touches the circle if $\frac { 4 } { 3 }$.

\ the equation of PB is y + 1 = $\frac { 4 } { 3 }$ (x + 2), i.e.,

4x – 3y + 5 = 0.

A point on PB is (–5, –5). Its image by the line y = –1 is

Pข(–5, 3). So, the equation of the incident ray PขP is

y – 3 = $\frac { 3 + 1 } { - 5 + 2 }$ (x + 5) or 4x + 3y + 11 = 0.